Answer :
To find which expression is equivalent to [tex]\( pq \)[/tex], let's look at each option one by one:
1. [tex]\( p + q \)[/tex]: This expression represents the sum of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to [tex]\( pq \)[/tex] because [tex]\( pq \)[/tex] refers to their product, not their sum.
2. [tex]\( n - 0 \)[/tex]: This expression simplifies to [tex]\( n \)[/tex]. It does not involve [tex]\( p \)[/tex] or [tex]\( q \)[/tex] at all, and therefore cannot be equivalent to [tex]\( pq \)[/tex].
3. [tex]\(\frac{p}{q}\)[/tex]: This is a division expression, where [tex]\( p \)[/tex] is divided by [tex]\( q \)[/tex]. This is different from [tex]\( pq \)[/tex], which denotes multiplication.
4. [tex]\( qp \)[/tex]: This expression represents [tex]\( q \times p \)[/tex], which due to the commutative property of multiplication, is equivalent to [tex]\( p \times q \)[/tex] or [tex]\( pq \)[/tex]. Therefore, [tex]\( qp \)[/tex] is indeed the equivalent expression to [tex]\( pq \)[/tex].
Based on this analysis, the expression equivalent to [tex]\( pq \)[/tex] is [tex]\( qp \)[/tex].
1. [tex]\( p + q \)[/tex]: This expression represents the sum of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to [tex]\( pq \)[/tex] because [tex]\( pq \)[/tex] refers to their product, not their sum.
2. [tex]\( n - 0 \)[/tex]: This expression simplifies to [tex]\( n \)[/tex]. It does not involve [tex]\( p \)[/tex] or [tex]\( q \)[/tex] at all, and therefore cannot be equivalent to [tex]\( pq \)[/tex].
3. [tex]\(\frac{p}{q}\)[/tex]: This is a division expression, where [tex]\( p \)[/tex] is divided by [tex]\( q \)[/tex]. This is different from [tex]\( pq \)[/tex], which denotes multiplication.
4. [tex]\( qp \)[/tex]: This expression represents [tex]\( q \times p \)[/tex], which due to the commutative property of multiplication, is equivalent to [tex]\( p \times q \)[/tex] or [tex]\( pq \)[/tex]. Therefore, [tex]\( qp \)[/tex] is indeed the equivalent expression to [tex]\( pq \)[/tex].
Based on this analysis, the expression equivalent to [tex]\( pq \)[/tex] is [tex]\( qp \)[/tex].
