Question

Let A = {1,2} and B = {3,4}. Write A X B , How many subsets will A X B have? List them.

Answer 1

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 subsetsGIVEN: 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 subsetsGIVEN: 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