Talk:if and only if

Isn't this entry redundant? --Eean 05:05, 25 Dec 2004 (UTC)

Decomposition

The following are common logical equivalents (A and B can also be swapped in each): Composed expressions

1. A if and only if B
2. A ⇔ B
3. (A is necessary and sufficient for B) / (A is a necessary and sufficient condition for B)

Decomposed expressions (first phrases are all equivalent as well as second phrases

1. (A if B) and (A only if B)
2. (A if B) and (B if A)
3. (if B then A) and (if A then B)
4. (B ⇒ A) and (A ⇒ B)
5. (B ⇒ A) and (B ⇐ A)
6. (A is necessary for B) and (A is sufficient for B)

--Bequw → τ 15:29, 20 August 2010 (UTC)