Difference between revisions of "And"
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(Created page with "If <math>P</math> and <math>Q</math> are propositions, then "<math>P</math> and <math>Q</math>" is a proposition (written <math>P ∧ Q</math>); it is true if...") |
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| − | If <math>P</math> and <math>Q</math> are [[proposition]]s, then "<math>P</math> [[and]] <math>Q</math>" is a [[proposition]] (written <math>P [[∧]] Q</math>); it is true if both <math>P</math> and <math>Q</math> | + | If <math>P</math> and <math>Q</math> are [[proposition]]s, then "<math>P</math> [[and]] <math>Q</math>" is a [[proposition]] (written <math>P [[∧]] Q</math>); it is true if both <math>P</math> is true and <math>Q</math> is true. |
| − | {{:prove both}} | + | * {{:prove both}} |
| − | {{:use either}} | + | * {{:use either}} |
| − | {{:disprove and}} | + | * {{:disprove and}} |
Revision as of 13:52, 10 February 2018
If and are propositions, then " and " is a proposition (written ); it is true if both is true and is true.
To prove " and ", you can separately prove and then prove .
If you have already proved (or assumed) and , you can conclude . You can also conclude .
To disprove " and ", you must either disprove or disprove . Put another way, the logical negation of " and " is "not or not ".
