State True/False

Question

1. If f is bijective function then f^-1 is also bijective function.
2. If f is surjective function then f^-1 is a function but not surjective.
3. Inverse of a function 'f' is a function only when it is bijective.
4. If a relation R: X->Y is left total, then it must be a function.

Answer 1

1. True - Because if a relation is one-one and onto then it inverse will also be one-one and onto.

2. False- First if the function is surjective it's can't be possible. For an inverse function should be bijective.

3. True.

4. False

A relation R⊆X×Y is left-total iff :

(∀s∈X) (∃t∈Y) [(s,t)∈R](∀s∈X) (∃t∈Y) [(s,t)∈R]

that is, iff every element of X relates to some element of Y.

So, here there can be a case that two elements of X relate to the same element of Y.

So it can't be always function.

Please let me know if I am incorrect.

Comments

you didn't proof 1,2 and 3, simply you wrote the questions again indirectly