Step by step
The question
Question: make the truth table of p ↔ q.
1 Rows for p and q
Each letter can be true or false.
Two letters give 2 × 2 = 4 rows: every way they can go.
We make a table: a column for each letter, then a column for each part, from the inside out.
We write T for true and F for false.
p: the first half T, the second half F.
This way no row is missed.
q: T, F, T, F, down the column.
2 Column for p ↔ q
We read the double arrow as if and only if.
p ↔ q is true when both sides are the same: both T, or both F.
So it is T only in rows 1 and 4.
Careful!
Both false is the same, so F ↔ F is T.
The last column is the answer: when p ↔ q is true.
Top to bottom: T, F, F, T.
3 Check
Let's check row 2 by hand.
In row 2, p is true and q is false.
Put them in: T ↔ F.
It gives F, as in the table.
Right!
Let's look back.
First: rows for p and q.
Then: column for p ↔ q.
Last: check.