Advertisements
Advertisements
प्रश्न
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∩ B)' = A' ∪ B'
उत्तर
Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
A ∩ B = {2, 4, 6, 8} ∩ {2, 3, 5, 7}
= {2}
(A ∩ B)' = U - (A ∩ B)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2}
= {1, 3, 4, 5, 6, 7, 8, 9} ... (1)
A' = U - A
= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 9}
B' = U - B
= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}
= {1, 4, 6, 8, 9}
A' ∪ B'
= {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9}
= {1, 3, 4, 5, 6, 7, 8, 9} ... (2)
From (1) and (2), we have (A ∩ B)' = A' ∪ B'
APPEARS IN
संबंधित प्रश्न
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find A'
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find B'
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ C)'
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ B)'
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A')'
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (B -C)'
If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:
B = {d, e, f, g}
If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:
C = {a, c, e, g}
If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:
D = {f, g, h, a}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is an even natural number}
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∪ B)' = A' ∩ B'
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A'?
Fill in the blank to make the following a true statement:
A ∪ A' = _____
Fill in the blank to make the following a true statement:
Φ′ ∩ A = _____
Fill in the blank to make the following a true statement:
A ∩ A' = _____
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a positive multiple of 3}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a natural number divisible by 3 and 5}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a perfect square}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is perfect cube}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x + 5 = 8}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : 2x + 5 = 9}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x ≥ 7}
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x ∈ N and 2x + 1 > 10}
