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The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2?
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The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = ...
Solution:
To determine if the sets V, R, and S are equal to one another, we need to find the values of x that satisfy each set and compare them.
Set V: {x / x^2 = 0}
- The only value of x that satisfies this set is 0, since any non-zero number squared is positive.
- Therefore, V = {0}.
Set R: {x / x^2 + 2x = 0}
- We can factor out x from the equation: x(x + 2) = 0.
- This equation is satisfied when x = 0 or x = -2.
- Therefore, R = {0, -2}.
Set S: {x / x^2 + x - 2 = 0}
- We can factor the equation: (x+2)(x-1) = 0.
- This equation is satisfied when x = -2 or x = 1.
- Therefore, S = {-2, 1}.
Comparing the sets, we see that V = {0} is a subset of both R = {0, -2} and S = {-2, 1}. However, R and S are not equal to each other since they have different values. Therefore, the only value of x that satisfies all three sets is x = 0.
Answer: (d) none of these.
To determine if the sets V, R, and S are equal to one another, we need to find the values of x that satisfy each set and compare them.
Set V: {x / x^2 = 0}
- The only value of x that satisfies this set is 0, since any non-zero number squared is positive.
- Therefore, V = {0}.
Set R: {x / x^2 + 2x = 0}
- We can factor out x from the equation: x(x + 2) = 0.
- This equation is satisfied when x = 0 or x = -2.
- Therefore, R = {0, -2}.
Set S: {x / x^2 + x - 2 = 0}
- We can factor the equation: (x+2)(x-1) = 0.
- This equation is satisfied when x = -2 or x = 1.
- Therefore, S = {-2, 1}.
Comparing the sets, we see that V = {0} is a subset of both R = {0, -2} and S = {-2, 1}. However, R and S are not equal to each other since they have different values. Therefore, the only value of x that satisfies all three sets is x = 0.
Answer: (d) none of these.
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The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = ...
(b) -2
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The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2?
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The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2?.
The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sets V = {x / x 2=0}, R={x / x^2 2x=0} and S = {x : x^2 x - 2 = 0) are equal to one another if x is equal to (b) -2 (c) 2 (d) none of these (a) 1/2?.
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