Advertisements
Advertisements
प्रश्न
If K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h} then find the following:
(K ∩ L) ∪ (K ∩ M) and verify distributive laws
उत्तर
K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}
(K ∩ L) ∪ (K ∩ M)
(K ∩ L) = {b, d)
(K ∩ M) = {a, b, d}
(K ∩ L) ∪ (K ∩ M) = {b, d} ∪ {a, b, d} = {a, b, d}
Distributive laws
K ∪ (L ∩ M) = (K ∪ L) ∩ (K ∪ M)
{a, b, c, d, e, f) = {a, b, c, d, e, f, g} ∩ {a, b, c, d, e, f, h}
= {a, b, c, d, e, f}
Thus Verified.
K ∩ (L ∪ M) = (K ∩ L) ∪ (K ∩ M)
{a, b, d} = {a, b, c, d, e, f, g} ∪ {a, b, c, d, e, f, h}
= {a, b, d}
Thus Verified.
APPEARS IN
संबंधित प्रश्न
Using the adjacent Venn diagram, find the following set:
A’ ∪ B’
Using the adjacent Venn diagram, find the following set:
(B ∪ C)’
Using the adjacent Venn diagram, find the following set:
A – (B ∩ C)
If K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h} then find the following:
K ∪ (L ∩ M)
If A = {x : x ∈ Z, −2 < x ≤ 4}, B = {x : x ∈ W, x ≤ 5}, C = {− 4, −1, 0, 2, 3, 4} verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) using Venn diagrams
If A = {– 2, 0, 1, 3, 5}, B = {–1, 0, 2, 5, 6} and C = {–1, 2, 5, 6, 7}, then show that A – (B ∪ C) = (A – B) ∩ (A – C)
If A = `{y : y = ("a"+1)/2, "a" ∈ "W" and "a" ≤ 5}`, B = `{y : y = (2"n" – 1)/2, "n" ∈ "W" and "n" < 5}` and C = `{-1, −1/2, 1, 3/2, 2}` then show that A – (B ∪ C) = (A – B) ∩ (A – C)
Verify A – (B ∩ C) = (A – B) ∪ (A – C) using Venn diagrams
Verify (A ∩ B)’ = A’ ∪ B’ using Venn diagrams
