Advertisements
Advertisements
प्रश्न
Use the properties of sets to prove that for all the sets A and B
A – (A ∩ B) = A – B
उत्तर
We have
A – (A ∩ B) = A ∩ (A ∩ B)′ .....(Since A – B = A ∩ B′)
= A ∩ (A′ ∪ B′) ......[By De Morgan’s law]
= (A ∩ A′) ∪ (A ∩ B′) ......[By distributive law]
= φ ∪ (A ∩ B′)
= A ∩ B′
= A – B
APPEARS IN
संबंधित प्रश्न
For all sets A, B and C is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.
For all sets A, B, and C
Is (A – B) ∩ (C – B) = (A ∩ C) – B? Justify your answer.
Let A, B and C be sets. Then show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Let P be the set of prime numbers and let S = {t | 2t – 1 is a prime}. Prove that S ⊂ P.
From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the largest possible number that could have passed all three examination?
The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to ______.
For all sets A, B and C, show that (A – B) ∩ (A – C) = A – (B ∪ C)
