Question

Question 3 Consider the statement: For any a, beR, if a is rational and b is rational then a/b is rational. Write the statement with predicate logic. Then negate the predicate logic statement. Translate your negation into a sentence

Answer 1

Let us assume that:

R(x) denotes x is a rational

R(a) -> a is a rational
R(b) -> b is a rational
R(a/b) -> a/b is a rational

Translating the given statement into Predicate logic: (R(a) ^ R(b)) -> R(a/b)  

Applying Negation: ~((R(a) ^ R(b)) -> R(a/b))

Expanding terms: ~( ~(R(a) ^ R(b)) v R(a/b) )

Expanding terms: ~( ~R(a) v ~R(b) v R(a/b) )

Expanding terms: R(a) ^ R(b) ^ ~R(a/b)

Translating negation into sentence:

a is rational and b is rational and a/b is not a rational