# Syntax in propositional logic — exercises

Syntax in propositional logic Exercises

Syntax-in-propositional-logic-Exercises-solutions

Fill in the truth tables for the operators

p    q          p . q          p v q        p ﬤ q        p ≡ q        ~p

T    T

T    F

F    T

F    F

Calculate the truth value of these statements

1. ~[(A v B) (D   > E)]

f     t        f         f

1. (A > C) v [(H > G) > (N v M)]

f     t           t     f           t       t

1. [(F > B)   v (K v G)] ~ P

t     t           f     f           t

[(A v B) > (~B > A)] > [(A • B) • (~B• ~A)]

t     f              f     t             t     f           f       t

Name the kind of statement each is, or circle errors that make it unreadable.

Assuming that A, C and H, and R are true, and that B, D, and J are false, calculate the truth value when possible.

1. (A v B) > (C ~D) v H

1. A v [B > (C . ~D)] v H

1. [(A v B) > (C v ~D)] v H

1. (A v B) > (C ~D) ≡ H ~ v (R . J)

1. (A v B) > (C ~D) ≡ H v (R . J)

1. [(A v B) > (C ~D)] ≡ [H v (R . J)]

1. {[(A v B) > (C > D)] ≡ H} v (R . J)

1. (A v B) > {[(~C v ~D) ≡ H] v (R . J)}

1. [(A v B)] > {(C > D) ≡ [H v (R > J)]}

1. {(A v B) > [(C ~D) ≡ H]} > (R ≡ J)