Use ∈ or ∉ to indicate whether the given object is an element of the given set in the following problems. 12 {1, 2, 3, 4, . . . }

QUESTION 10 Consider the following statements: T(x, y): "x eats y". A(x): "x is wise". S(x): "x is hungry". F(y): "y is fat". H(y): "y is healthy". The domain of x is the set of all people and the domain of y is the set of all food. Select the symbolic of the following statement: "Mike is hungry and wise but do not eat all healty food" None of the proposed answers. Vy A (Mike) AS (Mike ) V [H (y) ^ ¬T(x,y)] 3y A (Mike ) AS (Mike) ^[H (y) → ¬T(x,y)] Vy A (Mike) A S (Mike) V [H (y) → ¬T(x,y)] Vy A (Mike) AS (Mike) ^[H (y) → ¬T(x,y)]

7. Find the union or intersection as indicated for the given sets.A = {x | x ∈ the natural numbers and x < 4}, B = {x | x ∈ the integers and -2 < x < 2}Find A ∪ B. A.{0, 1} B.{-2, -1, 0, 1, 2, 3, 4} C.{-1, 0, 1, 2, 3} D.{1} E.No answer text provided.

Can you break these 3 questions down in a step by step so I can understand. 1. Find two sets A and B such that E B and A ≤ B. 2. Show that if A ≤ C and B≤ D, then A*B ≤ C*D 3. Let A, B, and C be sets. Show that (A-B) - C ≤ A-C