Question

A,b€ Q then (a×b) € _______
2) a,b€ Q then ( a-b) € ______
3) a,b€ Q then ( a/b ) € ______
4) a,b € Q then ( a+b) € _______
Please ans fast I need help

Answer 1

Answer:

Answer

Correct option is

B

2

pq

Given A and B are two sets with number of elements p and q respectively.

The cartesian product of A and B=A×B={(a,b):(a∈A) and (b∈B)}

Number of elements in A×B=∣A×B∣=∣A∣.∣B∣=pq

Any relation from A to B is a subset of A×B.

Hence number of relations from A to B is the number of subsets of A×B

=2

∣A×B∣

=2

pq

hope it helps you✌

Answer 2

Answer:

(i)  a∗b=a−b

Check commutative is

a∗b=b∗a

a∗b=a−b

b∗a=b−a

Since, a∗b=b∗a

∗ is not commutative.

Check associative

∗ is associative if

(a∗b)∗c=a∗(b∗c)(a∗b)∗c=(a−b)∗c=(a−b)−c=a−b−ca∗(b∗c)=a∗(b−c)=a−(b−c)=a−b+c

Since (a∗b)∗c=a∗(b∗c)

∗ is not an associative binary operation.

(ii)  a∗b=a2+b2

Check commutative

∗ is commutative if a∗b=b∗a

a∗b=a2+b2b∗a=b2+a2=a2+b2

Since a∗b=b∗a∀a,bϵQ

∗ is commutative.

Check associative

∗ is associative if

(a∗b)∗c=a∗(b∗c)(a∗b)∗c=(a2+b2)∗c=(a2+b2)2+c2a∗(b∗c)=a∗(b2+c2)=a