Let-P-and-Q-be-statements-If-P-Q-is-true-then-P-Q-is-false-True-or-False-

Question Number 43434 by Joel578 last updated on 10/Sep/18

$$\mathrm{Let}\:{P}\:\mathrm{and}\:{Q}\:\mathrm{be}\:\mathrm{statements}.\:\mathrm{If}\:\left(\sim{P}\right)\:\vee\:{Q}\:\mathrm{is}\:\mathrm{true}, \\ $$$$\mathrm{then}\:{P}\:\:\vee\:{Q}\:\mathrm{is}\:\mathrm{false}. \\ $$$$\mathrm{True}\:\mathrm{or}\:\mathrm{False}? \\ $$

Commented by Joel578 last updated on 10/Sep/18

$$\mathrm{From}\:\mathrm{truth}\:\mathrm{table},\:\mathrm{if}\:\left(\sim{P}\right)\:\vee\:{Q}\:\mathrm{is}\:\mathrm{true},\:\mathrm{then}\: \\ $$$${P}\:\vee\:{Q}\:\mathrm{can}\:\mathrm{be}\:\mathrm{true}\:\mathrm{and}\:\mathrm{also}\:\mathrm{false}. \\ $$$$\mathrm{So},\:\mathrm{the}\:\mathrm{statement}\:\mathrm{in}\:\mathrm{the}\:\mathrm{question}\:\mathrm{should}\:\mathrm{be}\:\mathrm{true} \\ $$$$\mathrm{or}\:\mathrm{false}? \\ $$

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