# SETS

## By Prof. Masood Amir

### Past Papers from Karachi Board: XI Mathematics

1992.Q.1.(a) (i) IF A={2,3}, B={3,4} AND C={4,5}, Prove that

Ax(BΠC) =(AxB)Π(AxC)

1992.Q.1(a)  Let U = {0,1,2,3}, A={0,1), B={1,2}, C={2,3), then prove that

Ax(BUC) = (AxB)U(AxC)

1993. Q.1 (b) Let S={A,B,C,D}, where A={1}, B={1,2}, C={1,2,3} and D=φ

Construct the multiplication tables to show that U and Π are binary operations on S.

1994. Q.1. (a) IF U={1,2,3,4,5,6}, A={1,2,3}, B={1,3,5} and C={2,4,6}, Find A-C, and verify

That A Π B is a subset of A and A is a subset of AUB

1995. Q,1. (c) State De Morgan’s Law and verify it when A={3,4}, B={3,5} & U={1,2,3,4,5}

1996. Q.1. (d) Let A={0,1,2,4} Define a*b=a Ѵ a,b є A. Construct table for * in A

1997 Q.1. (a) Verify the property Ax(BUC)=(AxB)U(AxC) in the following sets   A={a,b}, B={b,c}, C={c,d}

1998 Q.1. (a) Let A={0,2,4}, B={1,2} and C={3,4} then prove that            Ax(BUC)=(AxB)U(AxC)

1999 Q.1. (a) Let U={1,2,3,4,5,6}, A={1,2,3,4}, B={1,3,4,5}

show that (A Π B)’ = A’ U B’

2000 Q.1. (a) Let U={2,3,4,5,6}, A={2,1}, B={3,4}, C={4,5}

Show that (B-C)’ = B’

2003 Q.1. (a) If A={2,3}, B={3,4}, C={c,f} and U={2,3,4,c,f} find (AxB)U(AxC) and B’-A’.

2004 Q.1. (a) If A={1,2,4}, B={2,3,4}, U={1,2,3,4,5} find (AUB)’ and

(A Π A’)’

2005 Q.1. (a) If A and B are the subsets of the universal set. Then prove that

AUB = AU(A’nB)

2006 Q.1. (a) If A and B are the subsets of the universal set. Then prove that

AUB = AU(A’nB)

2007 Q.1. (a) If U={a,b,c,d,e}, A={a,b,c}, B={b,c,d}, find (AnB)

2008 Q.1. (a) If A={2,3}, B={3,4}, C={4,5}, find Ax(BUC)

Cont……………………..d