Question

Construct a truth table for the given statement.mnFill in the truth table.װן--mnTFFTFF

Answer 1

The symbol V is read as 'OR'.

Hence, pVq is read as p or q.

If p or q is true(T), then pVq is also true(T).

The truth table for pVq is,

p. q. pVq

T. T. T

T. F. T

F. T. T

F. F. F

The symbol ˜ is read as negation.

˜q means the opposite of q. If q is true(T), then ˜q is false(F) and vice versa.

p. q. pVq ˜q

T. T. T F

T. F. T T

F. T. T F

F. F. F T

The symbol <-> is read as if and only if.

(pVq) <-> ˜q implies that pVq is true if and only if ˜q is true.

(pVq) <-> ˜q is the truth value of pVq only if ˜q is true (T) and the value of (pVq) <-> ˜q is the opposite of the truth value of pVq if ˜q is false (F).

p. q. pVq ˜q (pVq) <-> ˜q

T. T. T F F

T. F. T T T

F. T. T F T

F. F. F T F

The truth table is

p. q. pVq (pVq) <-> ˜q

T. T. T F

T. F. T T

F. T. T T

F. F. F F