Question

How many rows appear in a truth table for the compound proposition: \[(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r) \wedge \neg q\]

Answer 1

Let me re-write the proposition:

p↔q⊕(¬p↔¬r)∧¬q.

Generally, the number of rows in a truth table depends on the number of Variables. Here we have 3 Variables: p,q and r. Each of them can have either the value of 1 or 0, which gives us 2*2*2 possibilities, or 2³, that is 8 possibilities and 8 rows:

p=0, q=0, r=0
p=0, q=0, r=1
p=0, q=1, r=0
p=0, q=1, r=1
p=1, q=0, r=0
p=1, q=0, r=1
p=1, q=1, r=0
p=1, q=1, r=1