Question

Identify the correct translation into logical notation of the following assertion. Some boys in the class are tallerr than all the girls
Note: Taller (x, y) is true if x is taller than y .

• A. $\left(\exists x\right)(boy\left(x\right)\to \left(\forall y\right)(girl\left(y\right)\wedge taller(x,y)))$
• B. $\left(\exists x\right)(boy\left(x\right)\wedge \left(\forall y\right)(girl\left(y\right)\wedge taller(x,y)))$
• C. $\left(\exists x\right)(boy\left(x\right)\to \left(\forall y\right)(girl\left(y\right)\to taller(x,y)))$
• D. $\left(\exists x\right)(boy\left(x\right)\wedge \left(\forall y\right)(girl\left(y\right)\to taller(x,y)))$

Answer 1

The correct option is D $\left(\exists x\right)(boy\left(x\right)\wedge \left(\forall y\right)(girl\left(y\right)\to taller(x,y)))$

The statement is " some boys in the class are taller than all the girls''.
So the notation for the given statement is $\left(\exists x\right)\left(boy\right(x)\wedge (\forall y\left)\right(girl\left(y\right)\to taller(x,y)\left)\right)$