4. Two marks exercise problems II

1. If $U = \{x : x \in \mathbb{N}, x \le 10\}$, $A = \{2, 3, 4, 8, 10\}$ and $B = \{1, 2, 5, 8, 10\}$, then verify that $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.

 

Proof:

 

LHS:

 

$n(A \cup B) =$

 

RHS:

 

$n(A) =$

 

$n(B) =$

 

$n(A \cap B) =$

 

$n(A) + n(B) - n(A \cap B)$ $=$

 

 

Hence, proved.

 

 

2. If $U = \{1, 2, 3, .., 10\}$, $P = \{3, 4, 5, 6\}$ and $Q = \{x : x \in \mathbb{N}, x < 5\}$, then verify that $n(Q - P) = n(Q) - n(P \cap Q)$.

 

Proof:

 

LHS:

 

$n(Q - P) =$

 

RHS:

 

$n(Q) =$ 

 

$n(P \cap Q) =$

 

$n(Q) - n(P \cap Q)$ $=$