A ↔ B — truth table

coretrue on the two agreeing rows

Answer

4 rows, 2 true (0, 3)

Why this example is worth doing

The biconditional is true exactly when both sides agree, which makes it the XNOR gate under a different name and from a different course. Seeing A ↔ B, A ⊙ B and (A ⊕ B)′ produce identical columns is the cleanest way to show a discrete-maths student and a digital-logic student that they are studying the same object. The page links across to the XNOR gate page for the circuit reading, and notes that equality comparators are literally trees of these.

Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.

How the answer is reached

Truth table

Truth table — columns #, A, B, A ↔ B
#	A	B	A ↔ B
0	0	0	1
1	0	1	0
2	1	0	0
3	1	1	1

Compare with

Open this example in the Truth table generator

The field arrives filled in with this example’s input.

Notation this page assumes

Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
In a minterm index the first variable is the most significant bit, so over [A, B, C] minterm 5 is A·B̄·C.

Sources

Boole, An Investigation of the Laws of Thought (1854)
Shannon, “A Symbolic Analysis of Relay and Switching Circuits” (1938)