Answer
How many rows appear in a truth table for each of these
compound propositions?
a) (q → ¬p) ∨ (¬p → ¬q) Ans: 4 rows
b) (p ∨ ¬t) ∧ (p ∨ ¬s) Ans: 8 rows
c) (p → r) ∨ (¬s → ¬t) ∨ (¬u → v) Ans: 64 rows
d) (p ∧ r ∧ s) ∨ (q ∧ t) ∨ (r ∧ ¬t) Ans: 32 rows
Work Step by Step
First all, here is the famous quote from most textbook similarly written, "Any True Table Composed of n( number of propositions) distinct statement has 2^n rows", the formula to find number of rows the formula we used is 2^n
a) We have two different propositions in this case which are q and p (¬p and p counted as 1 even though they are different but they are same proposition), so 2^(2) is 4.
b) In this case we now have three different propositions -- p, t, s; so 2^(3) =8 rows
c) In this case we now have six different propositions -- p, r, s, t, u, v; so 2^(6) =64 rows
d) In this case we now have five different propositions -- p,r,s,q,t; so 2^(5) =32 rows
