Question

n(U) = 70 n(A) = 58 n(B) = 32 n(AUB)’ = 6. Find :- a) n(A∩B) b) n(A – B) c) n(AUB) = d) n(A’∩B)

Answer 1

Answer:

It is given that: n(U) = 70 , n(A)=58 and  n(AUB)’ = 6

Using the formula: $n(A\cap B)=n(A)+n(B)-n(A\cup B)$

(a)

$n(A\cup B) = n(U) - n(A\cup B)'$

$n(A\cup B) = 70 - 6=64$

$n(A\cup B) = 64$

Using the above formula we have,

$n(A\cap B) = 58 + 32 - 64=90-64=26$

$n(A\cap B) = 26$.

(b)

Using formula: $n(A - B) = n(A) - n(A \cap B)$

$n(A-B) =58 - 26=32$

$n(A-B) = 32$.

(c)

$n(A\cup B) = 64$

(d)

Using formula:

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

$n(A' \cap B) =32-26=6$

$n(A' \cap B)=6$

Use can also see the results in Venn diagram below: