State converse, inverse, contrapositive of "for all y,..."

[flakine]

For the statement: For all real numbers y there exists a real number x such that xy<=y

a) Write the converse
b) Write the inverse
c) Write the contrapositive

Can someone please help?

 

[Deleted member 4993]

Re: Discrete Math

For the statement: For all real numbers y there exists a real number x such that xy<=y

a) Write the converse
b) Write the inverse
c) Write the contrapositive

Can someone please help?

This is a "If A then B" statement.

What is the definition of converse, inverse and contrapositive?

 

[flakine]

Re: Discrete Math

If y is real, than there exists an x such that xy<=y

A = y is real
B = there exists an x such that xy<=y

Converse: if there exists an x such that xy<=y then y is real
Inverse: If y is not real, than all x, xy<=y
Contrapostive: for all x, if xy>y then y is not real


?????????????

 

[pka]

Re: Discrete Math

For the statement: For all real numbers y there exists a real number x such that xy<=y.
a) Write the converse
b) Write the inverse
c) Write the contrapositive

In doing these always translate first.
If y is a real number then some real number times y is less than or equal to y.
Then (a) becomes “If there is a real number x such x times y is less than or equal y then y is real”.

(b) “No real number y is such that every real number times y is greater than y”.

(c) If no real number times y is greater than y then y is not real.