For the sets A = {a, b, c, d, e}, B = {a, c, e, g, n}, C = {b, c, d, e, n, w} and the universal set is U = {a, b, c, d, e, g, n, w}. Find

Question

For the sets A = {a, b, c, d, e}, B = {a, c, e, g, n}, C = {b, c, d, e, n, w} and the universal set is U = {a, b, c, d, e, g, n, w}. Find

(a) |A ∩ B ∩ C|

(b) C¯

(c) A¯∪(B − C)

Answer 1

(a)    |A| represents the cardinality of the set A. In simpler words, the number of elements that set A has.

For A∩B∩C , we find the elements which are in common with all three sets

So, A∩B∩C = {c, e}

Hence, |A∩B∩C|=2

(b) C¯ is defined as all the elements which are there in set U but not in set C

Hence, C¯={a,g}

(c) A¯ ={g, n, w} (From the above definition of complement)

B – C , known as difference of sets represents set of all elements which are there in B but not in C.

So, B – C = {a, g}

Hence, A¯∪ (B – C)={a, g, n, w}