1: Show that $p\leftrightarrow q $ and $(p\wedge q) \vee (\neg p \wedge \neg q)$are logically equivalent using
logically equivalent properties learned in class.
2: Let P(x; y) be the statement \x hates y" where the domain is the set of
all the people. Use quantiers to express each of the following statements:
1. Everybody hates Kung.
2. Everybody hates somebody.
3. There is somebody whom everybody hates.
4. Nobody hates everybody.
5. There is somebody whom Boy dose not hate.
6. There is somebody whom no one hates.
7. There is exactly one person whom everyone hates.
8. There are exactly two person whom Noo hates.
9. Everyone does not hate himself or herself.
10. There is someone who hate everyone besides himself or herself.
3: Determine whether $(\neg q\wedge (p\rightarrow q)\rightarrow \neg p)$ is tautology using logically
equivalent properties.
4.Problem 4 Let Q(x; y) be the statement "x+y = x-y". If the domain is the set of
integers, what are the truth values of the following? Brie
y describe your answer.
a) $Q(1,1)$
b) $Q(2,0)$
c) $\forall y Q(1,y)$
e) $\exists x \exists y Q(x,y)$
g) $\exists y \forall x Q(x,y)$
i) $\forall x \forall y Q(x,y)$
d) $\exists xQ(x,2)$
f) $\forall x\exists y Q(x,y)$
h)$\forall y\exists x Q(x,y)$
แล้วก็อยากถามว่าการสลับที่ $\forall x\exists y เป็น \exists y\forall x $
แล้วไม่เท่ากันอยากขอตัวอย่างสักหน่อยคับ
ขอบคุณมากคับ
