Using properties of sets, show that (i) A∪(A∩B)=A (ii) A∩(A∪B)=A
Open in App
Solution
Verified by Toppr
(i) To show: A∪(A∩B)=A We know that A⊂A ⇒A∩B⊂A ∴A∪(A∩B)⊂A ......(1) Also, A⊂A∪(A∩B) ............(2) ∴ From (1) and (2), A∪(A∩B)=A (ii) To show: A∩(A∪B)=A A∩(A∪B)=(A∩A)∪(A∩B) =A∪(A∩B) =A (by (i)) ⇒A∩(A∪B)=A
Was this answer helpful?
29
Similar Questions
Q1
Using properties of sets, show that (i) A∪(A∩B)=A (ii) A∩(A∪B)=A
View Solution
Q2
Using
properties of sets show that
(i) A
∪
(A ∩
B) = A (ii) A ∩
(A ∪
B) = A.
View Solution
Q3
Using properties of sets, show that
(i) A∪(A∩B)=A (ii) A∩(A∪B)=A.
View Solution
Q4
Using properties of sets show that: (i)A∪(A∩B)=A (ii)A∩(A∪B)=A
View Solution
Q5
Show that for any sets A and B, ( By using the properties of sets ) A=(A∩B)∩(A−B)