LOGIC DEFINITIONS

Question 1

“p”, “not p”. Donated by ¬𝑝

Answer 1

Let 𝑝 be a proposition. The truth Value of the negation of 𝑝, ¬𝑝, is the opposite of the truth Value of 𝑝.

Question 2

CONJUNCTION, Donated by 𝑝 ∧ 𝑞

Answer 2

Let 𝑝 and 𝑞 be propositions. The conjunction 𝑝 ∧ 𝑞 is true when both 𝑝 and 𝑞 are true and is false otherwise.

Question 3

Definition 3 – DISJUNCTION, Donated by 𝑝 ∨ 𝑞

Answer 3

Let 𝑝 and 𝑞 be propositions. The disjunction 𝑝 ∨ 𝑞 is false when both 𝑝 and 𝑞 are false and is true otherwise.

Question 4

Definition 4 - EXCLUSIVE OR, Denoted by 𝑝 ⊕ 𝑞

Answer 4

Let 𝑝 and 𝑞 be propositions. The exclusive or of 𝑝 and 𝑞, is the proposition that is true when exactly one of 𝑝 or 𝑞 is true and is false otherwise. – NOT BOTH

Question 5

Definition 5 – Conditional Statements, Donated by 𝑝 → 𝑞

Answer 5

The conditional statement 𝑝 → 𝑞 is the proposition “if 𝑝, then 𝑞.” The conditional statement 𝑝 → 𝑞 is false when 𝑝 is true and 𝑞 is false, and true otherwise.

Question 6

Conditional Statement:

Answer 6

“If p, then q”. Example: If you live in Los Angeles, then you live in California” = TRUE

Question 7

Converse

Answer 7

“If q, then p”. Example: If you live in California, then you Live in Los Angeles” = FALSE

Question 8

INVERSE:

Answer 8

If not¬𝑝, then not ¬q” Example: If you don’t live in Los Angeles, then you don’t live in California” = FALSE

Question 9

CONTRAPOSITIVE:

Answer 9

If not ¬q, then not ¬𝑝” Example: If you don’t live in California, then you don’t live in Los Angele’s” = TRUE

Question 10

BICONDITIONAL STATEMENT, Dondated by 𝑝 ↔ 𝑞

Answer 10

The biconditional statement 𝑝 ↔ 𝑞 is the proposition “𝑝 if and only if 𝑞.” The biconditional statement 𝑝 ↔ 𝑞 is true when 𝑝 and 𝑞 have the same truth values, and is false otherwise.