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## Main Question or Discussion Point

I'm a little stuck with these bad boys:

Let P(x) be the assertion “x is odd”, and let Q(x) be the assertion “x is twice an integer.” Determine whether the following statements are true:

1. (Vx ∈ Z)(P(x) ⇒ Q(x))

2. (Vx ∈ Z)(P(x)) ⇒ (Vx ∈ Z)(Q(x))

I don't get the statement at all; if x is odd then 2x ? maybe if x is odd then 2x is even ?

Is that what they're trying to say ?

and for me the quantifiers look the same.

(Vx ∈ Z) a-> b is same as (Vx ∈ Z) a -> (Vx ∈ Z)b

I don't understand the question at all.

Let P(x) be the assertion “x is odd”, and let Q(x) be the assertion “x is twice an integer.” Determine whether the following statements are true:

1. (Vx ∈ Z)(P(x) ⇒ Q(x))

2. (Vx ∈ Z)(P(x)) ⇒ (Vx ∈ Z)(Q(x))

**My attempt:**I don't get the statement at all; if x is odd then 2x ? maybe if x is odd then 2x is even ?

Is that what they're trying to say ?

and for me the quantifiers look the same.

(Vx ∈ Z) a-> b is same as (Vx ∈ Z) a -> (Vx ∈ Z)b

I don't understand the question at all.