Question

If U = {1, 2, 3, …., 10} , P = {3, 4, 5, 6} and Q = {x : x ∈N, x < 5}, then verify that n(Q – P) = n(Q) – n(P∩Q)

Answer 1

Given, U = {1, 2, 3, …., 10}
P = {3, 4, 5, 6}
and Q = {x : x ∈N, x < 5} also we can write it Q = {1, 2 , 3, 4}

Now, Q - P = set of Q in which elements of P doesn't exists
e.g., Q - P = {1, 2}
so, n(Q - P) = 2 [ because there are two elements in Q - P set ]

Now, Q = {1, 2, 3, 4}
n(Q) = 4 [ because there are four elements in Q]
P ∩ Q = set of common elements of P and Q ={3,4}
n(p ∩ Q} = 2

Now, LHS = n(Q - P) = 2
RHS = n(Q) - n(P ∩ Q) = 4 - 2 = 2
Hence, n(Q - P) = n(Q) - n(P ∩ Q) [ hence proved]