Mathematics Exam > Mathematics Questions > Let x, y and z be Boolean variables. The numb...
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Let x, y and z be Boolean variables. The number of possible values for the expression 
is
is- a)1
- b)2
- c)4
- d)8
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let x, y and z be Boolean variables. The number of possible values for...
The set of even natural numbers, {6,8,10,12,…}, is closed under addition operation. We are asked to identify the property it satisfies.
This set satisfies the closure property under addition since the sum of any two even numbers is also even.
This set satisfies the closure property under addition since the sum of any two even numbers is also even.
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Let x, y and z be Boolean variables. The number of possible values for...
So, The number of possible values for the expression
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Let x, y and z be Boolean variables. The number of possible values for...
Closure Property:
The closure property states that when two elements from a set are combined using a certain operation, the result will also be an element of the same set. In this case, the set of even natural numbers is closed under the addition operation.
Explanation:
To determine if a set is closed under addition, we need to check if the sum of any two elements in the set is also an element of the same set.
Let's take two even numbers from the given set: 6 and 8.
When we add these two numbers, we get 6 + 8 = 14. Now, we need to check if 14 is also an even number.
An even number is defined as an integer that is divisible by 2 without leaving a remainder. In other words, if we divide an even number by 2, the result will be an integer.
If we divide 14 by 2, we get 14/2 = 7, which is an integer. Therefore, 14 is also an even number.
Since the sum of any two even numbers from the given set is also an even number, we can conclude that the set of even natural numbers is closed under addition.
Conclusion:
The set of even natural numbers satisfies the closure property under the addition operation.
The closure property states that when two elements from a set are combined using a certain operation, the result will also be an element of the same set. In this case, the set of even natural numbers is closed under the addition operation.
Explanation:
To determine if a set is closed under addition, we need to check if the sum of any two elements in the set is also an element of the same set.
Let's take two even numbers from the given set: 6 and 8.
When we add these two numbers, we get 6 + 8 = 14. Now, we need to check if 14 is also an even number.
An even number is defined as an integer that is divisible by 2 without leaving a remainder. In other words, if we divide an even number by 2, the result will be an integer.
If we divide 14 by 2, we get 14/2 = 7, which is an integer. Therefore, 14 is also an even number.
Since the sum of any two even numbers from the given set is also an even number, we can conclude that the set of even natural numbers is closed under addition.
Conclusion:
The set of even natural numbers satisfies the closure property under the addition operation.
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