Question

Identify the rule of inference that is used to derive the conclusion "You do not eat tofu" from the statements "For all x, if x is healthy to eat, then x does not taste good," "Tofu is healthy to eat," and "You only eat what tastes good."

Answer 1

Answer:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )

Step-by-step explanation:

1) Tofu is healthy

2) Tofu is healthy to eat

3) Tofu eats what taste good

1a) For all x, if x is healthy to eat

2a) For all x, if x is not healthy to eat, then x does not taste good.

3a) For all x, if x is healthy to eat, then x is healthy to eat what tastes good

For all x in order to symbolize the statement

1(a)   2(a)  3(a)

If we use:

A(x): Tofu is healthy

B(x): Tofu is healthy to eat

C(x): Tofu eats what taste good

E(x): Tofu only eat what tastes good

If we symbolize "For all x" by the symbol ∀ then then the propositions 1(a), 2(a) and 3(a) can be written as:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )