# A word for when two statements are both true or both false

Is there a word which basically means that there are two statements that are both true, or both false, but not one true and one false? In computing, we call this a bitwise and.

``````3 * 3 = 9
4 * 4 = 16
``````

Both of those statements evaluate true, so I would want the word to apply here.

``````3 * 3 = 10
4 * 4 = 15
``````

Both of these statements evaluate false, so I would want the word to apply here as well.

``````3 * 3 = 9
4 * 4 = 15
``````

However, here, both statements disagree (one true, one false) and so the word shouldn't apply here.

Does such a word exist?

• "Both statements are true" satisfies the condition. Why do you need a single word? May 9 '14 at 14:56
• @KitFox, we're looking for a term that applies if both statements are true or if both statements are false, but not if one statement is true and the other is false. May 9 '14 at 15:00
• Look at the truth table for AND again. For that matter, you may want to look up the difference between bitwise AND and logical AND.
– user28567
May 11 '14 at 13:10
• You appear to need a ɴxᴏʀ (“nexxor”) operator in your language to go with your ɴᴀɴᴅ operator. Or just write `if (not (expr1 xor expr2)) { ... }` instead.
– tchrist
May 11 '14 at 14:27
• The reason why we needed a single word is because my friend is very difficult and requested one. I had already suggested 'logically equal' but he didn't quite like it. As he is using that word now though we can close this topic.
– Dan
May 12 '14 at 7:51

In logic seminar, we used to say that

Two statements have (or share) the same truth value.

If the statements always share the same truth value (either intrinsically or as a matter of empirical practice), then you could say either

Two statements always have (or share) the same truth value.

or

These two statements are logically equivalent.

(As per Jason above.)

In computing, we call this a bitwise and.

No, in computing this is called an "exclusive nor" or "XNOR".

In plain English, you could say that two statements are logically equal.

• "The result in each position is 1 if the first bit is 1 and the second bit is 1; otherwise, the result is 0." - bitwise AND from wikipedia. 01 & 01 will evaluate as 01, but 10 & 01 will evaluate as 10
– Dan
May 9 '14 at 13:55
• I doubt that they'll accept you as a member of the Plain English Campaign. May 9 '14 at 14:15
• Haha! I'm open to alternative wordings :D May 9 '14 at 14:29
• Call it "plainer" English, maybe, but this answer is accurate at least. We're hampered by the fact that in natural language we don't spend a lot of time comparing the truth of one statement to the truth of another. We don't have good, simple terms for it. May 9 '14 at 14:55
• @DanPantry 10 & 01 should evaluate to 00 May 9 '14 at 20:51

In mathematics, two statements that are either both true or both false are said to be equivalent. If the two statements are A and B, one might also say A if and only if B, or A iff B for short.

• It seems like only a logician could call "3 * 3 = 10" and "4 * 4 = 15" equivalent statements. Maybe you'd say they are "equally true"? May 9 '14 at 14:52
• @frances I'd call them equivalent. They are both indistinguishable from each other and reduce to "false". It becomes more interesting when there's a variable in it. For example you cannot say `3x=10` is equivalent to `4x=15`, because there exists values for x such that one is true and the other is not. You can however say that `3x=9` is equivalent to `4x=12` because for all values of x, both statements have the same truth value. It's just simply trivial for constant expressions. May 9 '14 at 19:51
• @frances And a slightly off-topic digression: In any programming language, replace all instances of (3*3==10) with (4*4==15) and your program will behave no differently May 9 '14 at 19:59
• @Cruncher - You're right from the logical point of view, I was just arguing that outside of that point of view, two false statements are not automatically equivalent, nor are two true statements. For instance, "my tea is cold" and "my wife is fat." One of those statements could get someone in more trouble than the other, regardless of whether their "truth" value is the same. May 9 '14 at 20:00
• @frances My personal refrain from calling these 2 things equivalent is the lack of objectivity. I can imagine a world where one of those is true and the other is false. I cannot imagine a world where one of `3*3=10` and `4*4=15` is true in base 10 using the standard interpretation of `*`. In fact we even employ this kind of reasoning regularly with stuff like: "Hey are you married?", with a reply of "Are you 3 feet tall and orange?" Using the obviously false statement to be equivalent to the question asked. May 9 '14 at 20:40

Both statements are in agreement

Both statements are synchronous.

The results of both statements are coupled.

Both statements are result equivalent. This is the most precise one. Also see nates answer.