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Use a membership table to show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

What is the symbolic word if Caroline is late (l), we will not pursue our plan (~p). We did not pursue our plan. Therefore, Caroline was late.

Show that the square of an even number is an even number using a direct proof.

Show whether or not p←→ q =(p→q) ^ (q→p)

Patrick has assignments in 5 subjects. He can only do two assignments . In how many ways can do two assignments?

Patrick has assignments in 5 subjects he can only do two assignments in how many ways can he do two assignments

How many 5 digit number can be formed from digits 0-6 if:

C. If one (1) is not to be used as the 1st digit and repetition is not allowed

### Let f and g be the functions defined by f(x)= 2x+3 g(x)= 3x+2 then composition of f and g is

Using proof by contraposition, show that if n is an integer and 5 added to its cube is odd then n is even. Before showing your solution, rewrite the statement to the proper form of a conditional statement then assign variables to the simple propositions. Show also the contrapositive form of the simple propositions before proceeding to your solution.

Use proof by contradiction to show that a number is even if its square is even. Before showing your solution, rewrite the statement to the proper form of a conditional statement. Assign variables to the simple propositions then write your assumption using these variables and logic symbols. At the end of your solution

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