Discrete Mathematics Answers

Show that  p⟷q and (p∧ q) V (¬p ∧ ¬q) are logically equivalent.

{x/x is an integer such as x² =2}

show in a truth table that p↔q and (p^q) v (¬p^¬q) are logically equivalent.

Let P (x) be the statement "x can speak Russian" and let

Q(x) be the statement "x knows the computer language

C++." Express each of these sentences in terms of P (x),

Q (x), quantifiers, and logical connectives. The domain

for quantifiers consists of all students at your school.

{x/x is an integer such as x² =2}

How many rows appear in a truth table for each of these

compound propositions?

a) (q -+ -'p) v (-'P -+ -.q)

b) (p v -.t) /\ (p v -'s)

c) (p -+ r) V (-,s -+ -.t) v (-,u -+ v)

d) (p /\ r /\ s) V (q /\ t) V (r /\ -.t)

Formulate the symbolic expression in English Sentence using p:Today is Monday. q:It is raining. r:It is hot.

4. ¬p → (q ˅ r)

5. ¬p → r

6. q → ¬r

1. Determine whether each of the following statements is a proposition or not. If it is, give its truth value.p: Mindanao is an island in the Philippines. 

• q: Find a number which divides your age. 
• r: My seatmate will get a perfect score in the Logic exam.
• s: Welcome to the Philippines!

show that "p \\leftrightarrow q" and "(p \\land q) \\lor (\\neg p \\land \\neg q)" are logically equivalent.

find the truth value "1\\land 1 \\to 1 \\lor 1"