Question

some elements of AXB are (1,7),(1,10),(3,12) if A={1,2,3} find the remaining elements of AXB such that n(AXB)is least​

Answer 1

Answer:

We know that,

domain of A×B belongs to A

range of A×B belongs to B

.

since,

A = {1,2,3}

and

(1,7),(1,10),(3,12) belongs to A×B

.

therefore,

we can say that,

{7,10,12} belongs to B

.

Now,

A×B = {1,2,3}×{7,10,12}

= {(1,7), (1,10), (1,12), (2,7), (2,10), (2,12), (3,7), (3,10), (3,12)}

and

n(A×B) = n(A)×n(B) = 3×3 = 9

.

.

Hope this helps :)

Answer 2

Answer:

9

Step-by-step explanation:

We know that,

domain of A×B belongs to A

range of A×B belongs to B

.

since,

A = {1,2,3}

and

(1,7),(1,10),(3,12) belongs to A×B

.

therefore,

we can say that,

{7,10,12} belongs to B

.

Now,

A×B = {1,2,3}×{7,10,12}

= {(1,7), (1,10), (1,12), (2,7), (2,10), (2,12), (3,7), (3,10), (3,12)}

and

n(A×B) = n(A)×n(B) = 3×3 = 9