Question

Question 1

Consider the following compound inequality:

-2 < x < 3

a) Explain why this compound inequality is actually a conjunction. Write this algebraic statement verbally.

b) Is the conjunction TRUE or FALSE when x = 3? Justify your answer logically (not algebraically!) by arguing in terms of truth values.

Question 2

Write verbally the negation of the following statement:

"Red mangos are always sweet while green mangos are sometimes sour."

Do not forget to apply De Morgan's laws here.

Question 3

Write symbolically a statement that has two components (p and q), is a tautology, and uses at least one disjunction, one conjunction and one negation.

Answer 1

Q1.

a) -2<X<3 is a conjuction since -2<X and X<3

When two statment is joined by "and" the compound statement is conjuction.

b) When X=3

-2<3 and 3<3 is False. Since 3<3 is False.

Q2. Given compund statement is

Red mangos are always sweet while green mangos are sometimes sour (P^Q)

P:Red mangos are always sweet

Q=green mangos are sometimes sour

Hence the statement pattern is Conjuction

hence

~(P^Q) = ~P V ~Q

that is : Red mangos are sometimes sweet or green mangos are always sour.

c)

[(pvq)^~q]v[~(pvq)] This statement pattern is a Tautology.