Q22 of 58 Page 12

Using properties of sets prove the statements given

Let . Is T an empty set? Justify your answer.

Given:


To check: T is an empty set or not







⇒ -(4x – 40)(13 – x) = (4x – 40)(x – 7)


⇒ (4x – 40)(x – 7) + (4x – 40)(13 – x) = 0


⇒ (4x – 40)(x – 7 + 13 – x) = 0


⇒ 6(4x – 40) = 0


⇒ 24(x – 10) = 0


⇒ x – 10 = 0


⇒ x = 10


So, T = {10}


⇒ T is not an empty set


More from this chapter

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Using properties of sets prove the statements given

For all sets A and B, A – (A ∩ B) = A – B

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Using properties of sets prove the statements given

For all sets A and B, (A ∪ B) – B = A – B

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Let A, B and C be sets. Then show that

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

 24

Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed

(i) in English and Mathematics but not in Science


(ii) in Mathematics and Science but not in English


(iii) in Mathematics only


(iv) in more than one subject only