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Answer :
To determine which expression is equivalent to [tex]\( p q \)[/tex], let's examine each option:
1. [tex]\( p + q \)[/tex]: This represents the addition of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to the expression [tex]\( p q \)[/tex], which involves multiplication, not addition.
2. [tex]\( p - q \)[/tex]: This represents the subtraction of [tex]\( q \)[/tex] from [tex]\( p \)[/tex]. It is also not equivalent to [tex]\( p q \)[/tex], as subtraction is not the same operation as multiplication.
3. [tex]\( \frac{p}{q} \)[/tex]: This represents the division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex]. Again, division is a different operation than multiplication, so this is not equivalent to [tex]\( p q \)[/tex].
4. [tex]\( q p \)[/tex]: This represents the multiplication of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. In mathematics, multiplication is commutative, meaning that the order of the factors does not matter. Therefore, [tex]\( q p \)[/tex] is the same as [tex]\( p q \)[/tex].
So, the expression that is equivalent to [tex]\( p q \)[/tex] is [tex]\( q p \)[/tex].
1. [tex]\( p + q \)[/tex]: This represents the addition of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to the expression [tex]\( p q \)[/tex], which involves multiplication, not addition.
2. [tex]\( p - q \)[/tex]: This represents the subtraction of [tex]\( q \)[/tex] from [tex]\( p \)[/tex]. It is also not equivalent to [tex]\( p q \)[/tex], as subtraction is not the same operation as multiplication.
3. [tex]\( \frac{p}{q} \)[/tex]: This represents the division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex]. Again, division is a different operation than multiplication, so this is not equivalent to [tex]\( p q \)[/tex].
4. [tex]\( q p \)[/tex]: This represents the multiplication of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. In mathematics, multiplication is commutative, meaning that the order of the factors does not matter. Therefore, [tex]\( q p \)[/tex] is the same as [tex]\( p q \)[/tex].
So, the expression that is equivalent to [tex]\( p q \)[/tex] is [tex]\( q p \)[/tex].
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