Essence Haskins

Consider the following compound inequality:

-2 < x < 3

a) This compound inequality is an example of a very common type of algebraic statement. Explain why it’s actually a conjunction. Write this algebraic statement verbally to justify your answer.

For x to satisfy this inequality x has to be greater than -2 and x has to be less than 3. Needs to justify both rules.

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

x=3

P=x;-2

Q= x;3

The inequality is p^q meaning that its a conjunction. It happens when x=3

3;-2 p is true 3=3 q is false

p q p^q

x=3 T F F

conjunction is false.

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.

p=red mangoes are sweet

q=some green mangoes are sour ~(p and q)

Some red mangoes are not sweet or all green mangoes are not sour.

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.

p q p^q ~p ~q ~p v ~q (p ^ q) v (~p v ~q)

T T T F F F T

T F F F T T T

F T F T F T T

F F F T T T T