Question

If A = { 1, 2 } &

B = { 3, 4 }

How many subsets will A × B have ? List them !!!

Relations and Functions || Class 11 CBSE || Maths

Answer 1

A = {1,2}
B = {3,4}

A×B = {(1,3),(1,4),(2,3),(2,4)}
.................
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subsets of A×B

{ }
{(1,3)}
{(1,4)}
{(2,3)}
{(2,4)}
{(1,3),(1,4)}
{(1,4),(2,3)}
{(2,3),(2,4)}
{(2,4),(1,3)}
{(1,3),(2,3)}
{(1,4),(2,4)}
{(1,3),(1,4),(2,3)}
{(1,4),(2,3),(2,4)}
{(2,3),(2,4),(1,3)}
{(2,4),(1,3),(1,4)}
{(1,3),(1,4),(2,3),(2,4)}

Answer 2

Answer:

GIVEN: A = {1,2}, B = { 3,4 }

TO FIND: The subsets of A x B (A cross B)

A x B = { (1,3), (1,4), (2,3), (2,4) }

So, A x B has 4 elements or 4 ordered pairs.

If we represent these elements or ordered pairs as p, q, r, s

S = { p,q,r,s }

Its subsets are

{ p}, { q } , {r} , {s} ,

{ p,q} , { p,r}, {p, s} , { q,r} , { q,s} , { r,s }

{ p, q, r} , { p, r, s} , { q,r,s} , { q, s, p}

{ p, q, r, s} &

Null set

the formula: no of subsets of A x B = 2^n, where n is the number of elements or ordered pairs belonging to A x B

So, the above A x B has 16 subsets

Step-by-step explanation:

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