# Can anybody explain this logical symbol?

I know this is not right place to post this question.

Please help me

I will notate & for "and" and ^ for "or"

[Editor: Instead, let's use MathJax to notate $\land$ for "and" and $\lor$ for "or" ]

$A$: I got A, $B$: I went to school.

$\neg(A\lor B)$ = Neither I got A nor did I go to school.

which is equivalent to $\neg A\land \neg B$ = I did not get A and I did not go to school.

But what I have trouble is

$\neg A\lor \neg B$ is I did not get A or I did not go to school.

which is equivalent to $\neg (A\land B)$ . but , I do not know how to translate $\neg (A\land B)$ into english sentence.

Can anyone help me?

Also, what is the difference between "Both I love 1 and I love 2" and "I love both 1 and 2"

are both sentences equal to $A\land B$ ?

• Why not use $\vee$ for "or"? – graydad Sep 24 '14 at 4:21
• Please use MathJax. $\land$ is $\land$, $\lor$ is $\lor$, $\neg$ is $\neg$, and so: $\neg (A\lor B)=\neg A\land\neg B$ is $\neg (A\lor B)=\neg A\land \neg B$ – Graham Kemp Sep 24 '14 at 4:24

## 1 Answer

I did not get A or I did not go to school $\iff$ It is not the case that I got an A and went to school

• Is that the translation of ~(A&B) ? – aaa Sep 24 '14 at 4:26
• Yes it is. Also I encourage you to use $\wedge$ for "and", while saving $\vee$ for "or". That is the standard syntax. – graydad Sep 24 '14 at 4:27
• Thanks for reply, but is there another way to transcribe it? besides using "it is not the case" – aaa Sep 24 '14 at 4:40
• I didn't get an A and go to school – graydad Sep 24 '14 at 4:44
• Since English is not my native language, I think I didn't get an A and go to school is same as I didn't get an A and I did not go to school. But, First sentence is ~(A&B) and second is ~A&~B, but they are not same, though. – aaa Sep 24 '14 at 6:24