Mixing
Fundamental Logical Operations are monotone with their variables.
$begingroup$
My question is more for understanding what i actually have to do.
So, i have to prove that
1)A ∧ B and A ∨ B are increasing monotone in relation with A and in relation with B
2)A ̅ is monotone decreasing in relation with A
3) A->B is monotone decreasing in relation with A and monotone increasing in relation with B
So i think that i have to prove those things, but i have no idea how, all i could find is that AND and OR are both monotone because if we change the input of one of the fields to the other truth value, the result will stay in the same direction.
boolean-algebra
asked Jan 30 at 20:19
XaviusXavius
11
$endgroup$
add a comment |
$begingroup$
My question is more for understanding what i actually have to do.
So, i have to prove that
1)A ∧ B and A ∨ B are increasing monotone in relation with A and in relation with B
2)A ̅ is monotone decreasing in relation with A
3) A->B is monotone decreasing in relation with A and monotone increasing in relation with B
So i think that i have to prove those things, but i have no idea how, all i could find is that AND and OR are both monotone because if we change the input of one of the fields to the other truth value, the result will stay in the same direction.
boolean-algebra
asked Jan 30 at 20:19
XaviusXavius
11
$endgroup$
add a comment |
$begingroup$
My question is more for understanding what i actually have to do.
So, i have to prove that
1)A ∧ B and A ∨ B are increasing monotone in relation with A and in relation with B
2)A ̅ is monotone decreasing in relation with A
3) A->B is monotone decreasing in relation with A and monotone increasing in relation with B
So i think that i have to prove those things, but i have no idea how, all i could find is that AND and OR are both monotone because if we change the input of one of the fields to the other truth value, the result will stay in the same direction.
boolean-algebra
asked Jan 30 at 20:19
XaviusXavius
11
$endgroup$
My question is more for understanding what i actually have to do.
So, i have to prove that
1)A ∧ B and A ∨ B are increasing monotone in relation with A and in relation with B
2)A ̅ is monotone decreasing in relation with A
3) A->B is monotone decreasing in relation with A and monotone increasing in relation with B
So i think that i have to prove those things, but i have no idea how, all i could find is that AND and OR are both monotone because if we change the input of one of the fields to the other truth value, the result will stay in the same direction.
boolean-algebra
boolean-algebra
asked Jan 30 at 20:19
XaviusXavius
11
asked Jan 30 at 20:19
XaviusXavius
11
asked Jan 30 at 20:19
XaviusXavius
11
asked Jan 30 at 20:19
XaviusXavius
11
asked Jan 30 at 20:19
XaviusXavius
11
11
add a comment |
add a comment |
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