Answer :
To determine which expression is equivalent to [tex]\(PQ\)[/tex], let's evaluate each option step-by-step:
1. Option 1: [tex]\(p+q\)[/tex]
- This expression represents the sum of [tex]\(p\)[/tex] and [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
2. Option 2: [tex]\(p-q\)[/tex]
- This expression represents the difference between [tex]\(p\)[/tex] and [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
3. Option 3: [tex]\(\frac{p}{q}\)[/tex]
- This expression represents the division of [tex]\(p\)[/tex] by [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
4. Option 4: [tex]\(qp\)[/tex]
- This expression represents the multiplication of [tex]\(q\)[/tex] and [tex]\(p\)[/tex], which is equivalent to [tex]\(pq\)[/tex].
- Multiplying [tex]\(q\)[/tex] and [tex]\(p\)[/tex] gives the same result as multiplying [tex]\(p\)[/tex] and [tex]\(q\)[/tex] due to the commutative property of multiplication (since [tex]\(pq = qp\)[/tex]).
Therefore, the expression that is equivalent to [tex]\(PQ\)[/tex] is [tex]\(qp\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{qp} \][/tex]
1. Option 1: [tex]\(p+q\)[/tex]
- This expression represents the sum of [tex]\(p\)[/tex] and [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
2. Option 2: [tex]\(p-q\)[/tex]
- This expression represents the difference between [tex]\(p\)[/tex] and [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
3. Option 3: [tex]\(\frac{p}{q}\)[/tex]
- This expression represents the division of [tex]\(p\)[/tex] by [tex]\(q\)[/tex].
- It does not match the multiplication of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex].
4. Option 4: [tex]\(qp\)[/tex]
- This expression represents the multiplication of [tex]\(q\)[/tex] and [tex]\(p\)[/tex], which is equivalent to [tex]\(pq\)[/tex].
- Multiplying [tex]\(q\)[/tex] and [tex]\(p\)[/tex] gives the same result as multiplying [tex]\(p\)[/tex] and [tex]\(q\)[/tex] due to the commutative property of multiplication (since [tex]\(pq = qp\)[/tex]).
Therefore, the expression that is equivalent to [tex]\(PQ\)[/tex] is [tex]\(qp\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{qp} \][/tex]
