Logic basic

Question

Let F (x,y) be the statement such as x can fool y .where the domain consists of all people in world .

Express following statement using quantifiers

Express following statement using quantifiers

1) Everybody can fool fred

2) Evelyn can fool everybody

3)Everybody can fool somebody

4)there is no one who can fool everybody

5)Everyone can be fooled by Somebody

6) No one can fool both Fred and Jerry

7)Nancy can fool exactly 2 person

8) There is exactly one person whom everybody can fool

9) non one can fool himself or herself

10 ) There is someone who can fool exactly one person beside himself or herself

Answer 1

is this correct ? please point out my mistakes :)

1) Everybody can fool fred

= ∀xF(x, Fred)

2) Evelyn can fool everybody

=∀yF(Evelyn, y )

3)Everybody can fool somebody

=∀x∃yF(x,y)

4)there is no one who can fool everybody

∀y∃x ∼ F(x,y)

5)Everyone can be fooled by Somebody

=∀y∃x((x!=y)⋀F(x,y))

6) No one can fool both Fred and Jerry

∀x∼(F(x,fred)⋀F(x,Jerry )

7)Nancy can fool exactly 2 person:

∃x∃y((x!=y)⋀F(Nancy,x)⋀F(Nancy,y)⋀∀w(F(Nancy,w)-->(w=x ⋁ w=y ))

8) There is exactly one person whom everybody can fool

∃y∀xF(x,y)

9) non one can fool himself or herself

∀x∼F(x,x)

10 ) There is someone who can fool exactly one person beside himself or herself

∀x∃!y(F(x,y) ⋀ (x!=y) ⋀ ∀wF(x,w)-->w=y))

Comments

6) No one can fool both Fred and Jerry

∀x∼(F(x,fred)⋀F(x,Jerry )

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8) There is exactly one person whom everybody can fool

∃!y∀xF(x,y)

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Oh yes thanks and rest all fine??

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4)∼∃x∀yf(x,y)

Is this one correct of not then please explain why!!