Q1if A,B,C are three sets then proove that A∩(B C)=(A∩B) (A∩C)

Q2let A,B, and C be the sets such that AUB=AUC and A∩B=A ∩C show that B=C

1. WHAT IS THAT TRIANGLE

If the equation is   A∩(BUC)=(A∩B)U(A∩C)           THEN THE ANSWER IS THIS

TO PROVE  A∩(BUC)=(A∩B)U(A∩C)

IF A= {1,2,3,4}   AND B= {3,4,5,6}    AND C={5,6,7,8}  THEN

BUC = {3,4,5,6,7,8}

A∩(BUC)= {3,4}

A∩B={3,4}                      and        A ∩C= { }

so     (A∩B)U(A∩C)= {3,4}

hence proved that  A∩(BUC)=(A∩B)U(A∩C)

2. AUB = AUC

by applying ∩B on both sides

(AUB) ∩B = (AUC) ∩B

B = (A∩B)U(C∩B)                                             ({BY DISTRIBUTIVE PROPERTY} JUST FOR UNDERSTANDING)

B = (A∩C)U(C∩B)                                             AS A∩B = A∩C (GIVEN)

B= C∩ (AUB)                                                      (BY TAKING C COMMON)

B= C∩ (AUC)                                                      AS AUB = AUC

B=C                                                                      HENCE PROVED