If A, B and C are any three sets, then A andtimes; (B andcup; C) is equal to:a)(A andtimes; B) andcup; (A andtimes; C)b)(A andcup; B) andtimes; (A andcup; C)c)(A andtimes; B) andcap; (A andtimes; C)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?

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ACT Exam > ACT Questions > If A, B and C are any three sets, then A &tim...

If A, B and C are any three sets, then A × (B ∪ C) is equal to:

a)
(A × B) ∪ (A × C)
b)
(A ∪ B) × (A ∪ C)
c)
(A × B) ∩ (A × C)
d)
None of the above

Correct answer is option 'A'. Can you explain this answer?

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If A, B and C are any three sets, then A × (B ∪ C) is equal ...

Given,
A, B and C are any three sets.
Now, A × (B ∪ C) = (A × B) ∪ (A × C)

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Adapted from “The Nose Tree” in German Fairy Tales and Popular Stories by Jacob Grimm and Wilhelm Grimm (trans. Taylor, ed. 1864)Then the king made known to all his kingdom, that whomever would heal her of this dreadful disease should be richly rewarded. Many tried, but the princess got no relief. Now the old soldier dressed himself up very sprucely as a doctor, and said he could cure her. Therefore, he chopped up some of the apple, and, to punish her a little more, gave her a dose, saying he would call to-morrow and see her again. The morrow came, and, of course, instead of being better, the nose had been growing on all night as before; and the poor princess was in a dreadful fright. So the doctor then chopped up a very little of the pear and gave it to her. He said that he was sure that it would help, and he would call again the next day. Next day came, and the nose was to be sure a little smaller. However, it was bigger than when the doctor first began to meddle with it.Then he thought to him, "I must frighten this cunning princess a little more before I am able to get what I want from her." Therefore, he gave her another dose of the apple and said he would call on the morrow. The morrow came, and the nose was ten times bad as before."My good lady," said the doctor, "Something works against my medicine and is to strong for it. However, I know by the force of my art that it is this, you have stolen goods about you. I am certain of it. If you do not give them back, I can do nothing for you."The princess denied very stoutly that she had anything of the kind."Very well," said the doctor, "you may do as you please, but I am sure I am correct. You will die if you do not own it." Then he went to the king, and told him how the matter stood."Daughter," said he, "send back the cloak, the purse, and the horn, that you stole from the right owners."Then she ordered her maid to fetch all three and gave them to the doctor, and begged him to give them back to the soldiers. The moment he had them safe, he gave her a whole pear to eat, and the nose came right. And as for the doctor, he put on the cloak, wished the king and all his court a good day and was soon with his two brothers. They lived from that time happily at home in their palace, except when they took an airing to see the world in their coach with their three dapple-grey horses.What is the proper form of the underlined selection, "known to all his kingdom, that"?

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Adapted from “The Nose Tree” in German Fairy Tales and Popular Stories by Jacob Grimm and Wilhelm Grimm (trans. Taylor, ed. 1864)Then the king made known to all his kingdom, that whomever would heal her of this dreadful disease should be richly rewarded. Many tried, but the princess got no relief. Now the old soldier dressed himself up very sprucely as a doctor, and said he could cure her. Therefore, he chopped up some of the apple, and, to punish her a little more, gave her a dose, saying he would call to-morrow and see her again. The morrow came, and, of course, instead of being better, the nose had been growing on all night as before; and the poor princess was in a dreadful fright. So the doctor then chopped up a very little of the pear and gave it to her. He said that he was sure that it would help, and he would call again the next day. Next day came, and the nose was to be sure a little smaller. However, it was bigger than when the doctor first began to meddle with it.Then he thought to him, "I must frighten this cunning princess a little more before I am able to get what I want from her." Therefore, he gave her another dose of the apple and said he would call on the morrow. The morrow came, and the nose was ten times bad as before."My good lady," said the doctor, "Something works against my medicine and is to strong for it. However, I know by the force of my art that it is this, you have stolen goods about you. I am certain of it. If you do not give them back, I can do nothing for you."The princess denied very stoutly that she had anything of the kind."Very well," said the doctor, "you may do as you please, but I am sure I am correct. You will die if you do not own it." Then he went to the king, and told him how the matter stood."Daughter," said he, "send back the cloak, the purse, and the horn, that you stole from the right owners."Then she ordered her maid to fetch all three and gave them to the doctor, and begged him to give them back to the soldiers. The moment he had them safe, he gave her a whole pear to eat, and the nose came right. And as for the doctor, he put on the cloak, wished the king and all his court a good day and was soon with his two brothers. They lived from that time happily at home in their palace, except when they took an airing to see the world in their coach with their three dapple-grey horses.Which is the best form of the underlined selection, "palace, except when they took an airing to see the world in their coach"?

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In a physics class, students conducted a series of experiments by placing different objects into a beaker of water. They conducted twenty trials for each object. For each trial, they recorded whether or not the object floated.First, they placed a steel paper clip into the water. They observed that the paper clip usually sank; however, they also saw that occasionally, the paper clip stayed afloat if it was placed very gently on top of the water. Next, they repeated the the same procedure using a cork, a toy boat made of aluminum, and a glass marble. They observed that both the cork and the toy boat always stayed afloat in the water, but that the glass marble always sank.Below, three students give their explanations for these observations.Student 1:Objects float when they are less dense than the liquid in which they are immersed. For example, when immiscible liquids of varying densities are mixed together in a container, the most dense liquid will sink to the bottom of the container, while the least dense liquid will rise to the top. This same principle applies to solid objects. Because the cork and the aluminum toy boat always float, cork and the aluminum of the boat must be less dense than water. Because the glass marble always sinks, the glass of the marble must be more dense than water.Objects that are more dense than water can also float due to surface tension. Surface tension occurs because molecules of a liquid are more attracted to each other more than they are to other objects. Molecules on the surface of water are attracted to the molecules around them and below them. This attraction causes a liquids surface to behave if it were covered by a thin film, which resists penetration by other objects. Therefore, small objects such as paper clips can sometimes float on water when the upward force of waters surface tension exceeds the force of gravity pulling such objects down. Because the paper clips often sink and only float sometimes, we can conclude that they are indeed more dense than water, and that their floating is due to surface tension.Student 2:Objects float in two different cases: when they are buoyed by a liquids surface tension or when their average density is less than that of the liquid in which they are immersed. The average density of cork is less than that of water. This is why the cork floats. In contrast, the density of glass is more than that of water. This is why the glass marble sinks.However, the densities of aluminum and of steel are greater than that of water. Thus, density cannot be used to explain why the aluminum toy boat and the paper clip float. Both of these objects float because of surface tension. Because the paper clip does not have much mass, the normal upward force created by waters surface tension can be enough to allow it to float. Other objects with greater mass, like the toy boat, employ a particular shape to magnify the force of surface tension. The curved shape of the boats bottom both stabilizes the boat and increases the amount of the boats surface area that touches the water, maximizing the force due to surface tension that the boat receives.Student 3:In this experiment, the paper clip floats because of surface tension; however, the cork, toy boat, and marble float or sink because of their relationship to a buoyant force. All objects immersed in a liquid experience a buoyant force, which pushes them upward. The strength of this force is equal to the weight of the liquid displaced, or pushed aside, by an object. Every object also experiences a downward force due to gravity, which is measured as the objects weight, and which is directly proportional to the objects mass. When the buoyant force acting on an object is greater than the downward force due to gravity, the object floats. However, when the buoyant force is less than the force due to gravity, the object sinks. Both the cork and the aluminum toy boat are able to displace enough water to create a buoyant force that exceeds the force due to gravity, so they float. However, the glass marble does not displace enough water to create a sufficient buoyant force, so it sinks.Q. The density of fresh, newly cut wood is less than water, and fresh wood always floats; however, over time, floating pieces of wood may sink. Which of the following explanations would Student 1 most likely give for this observation?

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In a physics class, students conducted a series of experiments by placing different objects into a beaker of water. They conducted twenty trials for each object. For each trial, they recorded whether or not the object floated.First, they placed a steel paper clip into the water. They observed that the paper clip usually sank; however, they also saw that occasionally, the paper clip stayed afloat if it was placed very gently on top of the water. Next, they repeated the the same procedure using a cork, a toy boat made of aluminum, and a glass marble. They observed that both the cork and the toy boat always stayed afloat in the water, but that the glass marble always sank.Below, three students give their explanations for these observations.Student 1:Objects float when they are less dense than the liquid in which they are immersed. For example, when immiscible liquids of varying densities are mixed together in a container, the most dense liquid will sink to the bottom of the container, while the least dense liquid will rise to the top. This same principle applies to solid objects. Because the cork and the aluminum toy boat always float, cork and the aluminum of the boat must be less dense than water. Because the glass marble always sinks, the glass of the marble must be more dense than water.Objects that are more dense than water can also float due to surface tension. Surface tension occurs because molecules of a liquid are more attracted to each other more than they are to other objects. Molecules on the surface of water are attracted to the molecules around them and below them. This attraction causes a liquids surface to behave if it were covered by a thin film, which resists penetration by other objects. Therefore, small objects such as paper clips can sometimes float on water when the upward force of waters surface tension exceeds the force of gravity pulling such objects down. Because the paper clips often sink and only float sometimes, we can conclude that they are indeed more dense than water, and that their floating is due to surface tension.Student 2:Objects float in two different cases: when they are buoyed by a liquids surface tension or when their average density is less than that of the liquid in which they are immersed. The average density of cork is less than that of water. This is why the cork floats. In contrast, the density of glass is more than that of water. This is why the glass marble sinks.However, the densities of aluminum and of steel are greater than that of water. Thus, density cannot be used to explain why the aluminum toy boat and the paper clip float. Both of these objects float because of surface tension. Because the paper clip does not have much mass, the normal upward force created by waters surface tension can be enough to allow it to float. Other objects with greater mass, like the toy boat, employ a particular shape to magnify the force of surface tension. The curved shape of the boats bottom both stabilizes the boat and increases the amount of the boats surface area that touches the water, maximizing the force due to surface tension that the boat receives.Student 3:In this experiment, the paper clip floats because of surface tension; however, the cork, toy boat, and marble float or sink because of their relationship to a buoyant force. All objects immersed in a liquid experience a buoyant force, which pushes them upward. The strength of this force is equal to the weight of the liquid displaced, or pushed aside, by an object. Every object also experiences a downward force due to gravity, which is measured as the objects weight, and which is directly proportional to the objects mass. When the buoyant force acting on an object is greater than the downward force due to gravity, the object floats. However, when the buoyant force is less than the force due to gravity, the object sinks. Both the cork and the aluminum toy boat are able to displace enough water to create a buoyant force that exceeds the force due to gravity, so they float. However, the glass marble does not displace enough water to create a sufficient buoyant force, so it sinks.Q.Paint is more dense than cooking oil; however, when a drop of paint is dripped into a container of cooking oil, it floats on top of the oil. If Student 1s explanation is correct, which of the following is most likely the reason for this observation?

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Directions:Read the passages and choose the best answer to each question.PassageAsian soybean rust (ASR) is a disease caused by the fungus Phakospora pachyrhizi. ASR spreads by windborne spores that infect soybean leaves. As rust lesions mature, they produce thousands of additional spores. Over time, large spore loads build up within ﬁelds and across large geographical areas. In 2004, this disease was detected in nine states in the American southwest, and by 2005 it had invaded several other states. ASR can drastically reduce crop yields in areas where it commonly occurs, so monitoring and application of preventive measures such as fungicide will likely be necessary.Certain fungicides have been tested for their effectiveness against ASR. These fungicides are listed in Table 1. The simplest classiﬁcation of fungicides divides them into three categories: contact, locally systemic, and systemic. Properties of these fungicide categories are given in Table 2.ASR infections generally begin in the lower leaf canopy where humidity is higher and leaves stay wet for longer periods. For this reason, the lower soybean leaf canopy is the primary spray target. Both upper and lower leaf surfaces must be sprayed. Coverage as dense as 400 spray droplets per square inch is considered ideal.The different properties of fungicide types have important implications for spray application. Contact and locally systemic fungicides require better spray coverage than systemic fungicides. Contact fungicides, because they do not penetrate the plant tissue, are more easily washed off the leaf by rain. This results in a shorter residual control period and more frequent re-application of the fungicide.Tests have shown that fungicides effectiveness varies based on the soybean growth stage at which the fungicide is applied. Figure 1 identiﬁes some of the different stages of soybean growth. Soybean leaves can be infected at any time with ASR. However, research has shown that the most critical time to protect soybean plants with fungicides is from the R1 through R5 growth stages. Fungicide applications should not be initiated after the R5 growth stage (seed development and mature plant).Q.Equal amounts of azoxystrobin, boscalid, and myclobutanil were applied to three different soybean plants during Growth Stage 3. After 24-hours, each of the plants was sprayed with water. Based on the data, which of the following represents the order, from least effective to most effective, of the fungicides’ likelihood of preventing ASR?

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If A, B and C are any three sets, then A × (B ∪ C) is equal to:a)(A × B) ∪ (A × C)b)(A ∪ B) × (A ∪ C)c)(A × B) ∩ (A × C)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?

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If A, B and C are any three sets, then A × (B ∪ C) is equal to:a)(A × B) ∪ (A × C)b)(A ∪ B) × (A ∪ C)c)(A × B) ∩ (A × C)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If A, B and C are any three sets, then A × (B ∪ C) is equal to:a)(A × B) ∪ (A × C)b)(A ∪ B) × (A ∪ C)c)(A × B) ∩ (A × C)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A, B and C are any three sets, then A × (B ∪ C) is equal to:a)(A × B) ∪ (A × C)b)(A ∪ B) × (A ∪ C)c)(A × B) ∩ (A × C)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.

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