Question

Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
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Answer 1

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(i) A = {2, 3}; B = {x: x is solution of x^2 + 5x + 6 = 0}

x^2 + 5x + 6 = 0 can be written as

x(x + 3) + 2(x + 3) = 0

By further calculation

(x + 2) (x + 3) = 0

So we get

x = –2 or x = –3

Here

A = {2, 3}; B = {–2, –3}

Therefore, A ≠ B

(ii) A = {x: x is a letter in the word FOLLOW} = {F, O, L, W}

B = {y: y is a letter in the word WOLF} = {W, O, L, F}

Order in which the elements of a set which are listed is not significant.

Therefore, A = B.

Answer 2

1. The A = {2, 3}; B = {x: x is solution of x² + 5x + 6 = 0} are not equal sets.

2. The A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF} are equal sets.

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Given that,

We have to prove the pair of sets are equal or not.

1. The given sets are A = {2, 3}; B = {x : x is solution of x² + 5x + 6 = 0}

Take the quadratic equation x² + 5x + 6 = 0

x² + 3x + 2x + 6 = 0

x(x+3) + 2(x+3) = 0

(x + 2)(x + 3) = 0

x=- 2 or x=- 3

B = {- 2, - 3}

But A = {2, 3}.

So, A ≠ B

2. The given sets are A = {x : x is a letter in the word FOLLOW}

And set B = {y : y is a letter in the word WOLF}

A = {F, L, O, W}; B = {W , O, L, F}

Both sets A and B share the same items.

So, A = B

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