Preliminary course for better foundations in Mathematics

Which Statement is correct in term of quantifiers and its negation " All the apples in the basket are ripe"

let A and B are two sets. If every element of A is also an element of B. then,

• A = B

• There is a human being y such that for every human being x, y is a father of x.

• For every human being x, there is a human being y such that y is a father of x.

• For every human being y, there is a human being x such that y is a father of x.

• Given any human being x, there exist a human being y such that y is a father of x.

The empty set is denoted as :

• 0

• {∅}

• ∅

(1,2) can be written in set builder form as :

• None of above.

Let A and B are two sets. A and B are equal if,

B^c ⊆ A^c if we have given

• A is empty

• one of A and B should be empty

• None

Let X and Y be non empty sets. A function f from X to Y is a map that assigns to each element in X, a unique element in Y. which is correct :

• None