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.
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