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Let M(x, y) be \"x has sent y an e-mail message\" and T(x, y) be...

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Advance Math

Let M(x, y) be \"x has sent y an e-mail message\" and T(x, y) be \"x has telephoned y, \" where the domain consists of all students inyour class. Use quantifiers to express each of thesestatements.

g. There is a student in your class who sent every one else inyour class an email message.

I answer  ∃x( x ≠ y ∧ ∀? M (x, y) )

But answer on text book is  ∃x( x ≠ y → ∀? M (x, y))

i. There are two different students in your class who fave senteach other e-mail messages.

I answer ∃x∃y( x ≠ y→ ∀? (M (x, y) ∧ M( y, x)))

But answer on text book is ∃x∃y( x ≠ y ∧ ∀? (M (x, y) ∧ M( y,x)))

I am confused about the use of → and ∧ on almost all thequestion.

Can someone explain two differences here, and perhaps explain itby translating to English?

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