Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following i

1.	Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following identities : (i)A∪(B∩C)=(A∪B)∩(A∪C) (ii) A∩(B∪C)=(A∩B)∪(A∩C) (iii) A∩(B−C)=(A∩B)−(A∩C) (iv) A−(B∪C)=(A−B)∩(A−C) (v) A−(B∩C)=(A−B)∪(A−C) (vi) A∩(BΔC)=(A∩B)Δ(A∩C)
Answer» Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following identities : $(i) A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ (ii) $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ (iii) $A \cap (B - C) = (A \cap B) - (A \cap C)$ (iv) $A - (B \cup C) = (A - B) \cap (A - C)$ (v) $A - (B \cap C) = (A - B) \cup (A - C)$ (vi) $A \cap (B Δ C) = (A \cap B) Δ (A \cap C)$

Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following identities : (i)A∪(B∩C)=(A∪B)∩(A∪C) (ii) A∩(B∪C)=(A∩B)∪(A∩C) (iii) A∩(B−C)=(A∩B)−(A∩C) (iv) A−(B∪C)=(A−B)∩(A−C) (v) A−(B∩C)=(A−B)∪(A−C) (vi) A∩(BΔC)=(A∩B)Δ(A∩C)

Answer»

Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following identities :

$(i) A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

(ii) $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$

(iii) $A \cap (B - C) = (A \cap B) - (A \cap C)$

(iv) $A - (B \cup C) = (A - B) \cap (A - C)$

(v) $A - (B \cap C) = (A - B) \cup (A - C)$

(vi) $A \cap (B Δ C) = (A \cap B) Δ (A \cap C)$