Difference between revisions of "And"

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[[Category:Proof techniques]]
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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> is true and <math>Q</math> is true.
 
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.
  

Latest revision as of 18:54, 17 February 2018


If [math]P [/math] and [math]Q [/math] are propositions, then "[math]P [/math] and [math]Q [/math]" is a proposition (written [math]P \href{/cs2800/wiki/index.php/%E2%88%A7}{∧} Q [/math]); it is true if both [math]P [/math] is true and [math]Q [/math] is true.

To prove "[math]P [/math] and [math]Q [/math]", you can separately prove [math]P [/math] and then prove [math]Q [/math].

If you have already proved (or assumed) [math]P [/math] and [math]Q [/math], you can conclude [math]P [/math]. You can also conclude [math]Q [/math].

To disprove "[math]P [/math] and [math]Q [/math]", you must either disprove [math]P [/math] or disprove [math]Q [/math]. Put another way, the logical negation of "[math]P [/math] and [math]Q [/math]" is "not [math]P [/math] or not [math]Q [/math]".