Answer :
To find which expression is equivalent to [tex]\( P q \)[/tex], let's analyze each option one by one:
1. Option 1: [tex]\( p + q \)[/tex]
This option represents the addition of [tex]\( p \)[/tex] and [tex]\( q \)[/tex], so it does not involve multiplication. Therefore, it is not equivalent to [tex]\( P q \)[/tex].
2. Option 2: [tex]\( p - q \)[/tex]
This option represents the subtraction of [tex]\( q \)[/tex] from [tex]\( p \)[/tex], which is also not related to multiplication. Hence, it is not equivalent to [tex]\( P q \)[/tex].
3. Option 3: [tex]\( \frac{p}{q} \)[/tex]
This option involves division, representing [tex]\( p \)[/tex] divided by [tex]\( q \)[/tex]. Since [tex]\( P q \)[/tex] indicates multiplication, this option is not equivalent.
4. Option 4: [tex]\( q p \)[/tex]
This option is the multiplication of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. In mathematics, multiplication is commutative, which means that the order of multiplication does not matter ([tex]\( a \times b = b \times a \)[/tex]). Therefore, [tex]\( q p \)[/tex] is equivalent to [tex]\( P q \)[/tex].
Based on this analysis, the expression that is equivalent to [tex]\( P q \)[/tex] is [tex]\( q p \)[/tex], which corresponds to the fourth option.
1. Option 1: [tex]\( p + q \)[/tex]
This option represents the addition of [tex]\( p \)[/tex] and [tex]\( q \)[/tex], so it does not involve multiplication. Therefore, it is not equivalent to [tex]\( P q \)[/tex].
2. Option 2: [tex]\( p - q \)[/tex]
This option represents the subtraction of [tex]\( q \)[/tex] from [tex]\( p \)[/tex], which is also not related to multiplication. Hence, it is not equivalent to [tex]\( P q \)[/tex].
3. Option 3: [tex]\( \frac{p}{q} \)[/tex]
This option involves division, representing [tex]\( p \)[/tex] divided by [tex]\( q \)[/tex]. Since [tex]\( P q \)[/tex] indicates multiplication, this option is not equivalent.
4. Option 4: [tex]\( q p \)[/tex]
This option is the multiplication of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. In mathematics, multiplication is commutative, which means that the order of multiplication does not matter ([tex]\( a \times b = b \times a \)[/tex]). Therefore, [tex]\( q p \)[/tex] is equivalent to [tex]\( P q \)[/tex].
Based on this analysis, the expression that is equivalent to [tex]\( P q \)[/tex] is [tex]\( q p \)[/tex], which corresponds to the fourth option.
