Question

if n(p) =8 and n(q) =5 find maximum and minimum number elements in p union q​

Answer 1

Given :-

• n ( P) = 8
• n ( Q) = 5

To find :-

• maximum no. of elements in P ∪ Q
• minimum no. of elements in P ∪ Q

Solution :-

As we know,

→ n(P ∪ Q) = n(P) + n(Q) - n(P ∩ Q)

so,

→ n(P ∪ Q) = 8 + 5 - n(P ∩ Q)

→ n(P ∪ Q) = 13 - n(P ∩ Q)

Now,

∵ The minimum no. of elements in P∩Q is zero, when P and Q are disjoint sets.

∴ maximum no. of elements in P∪Q =13 - 0

                                                                = 13

and

∵ The maximum no. of elements in P∩Q is 5,when all the elements of set Q are present in set P

∴ Minimum no. of elements in P∪Q = 13 - 5

                                                              = 8 .

Therefore,

Minimum no. of elements in P ∪ Q = 8

maximum no. of elements in P ∪ Q = 13

so,

we can say that

8 ≤ n ( P∪Q ) ≤ 13 .