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A-C-is-false-B-C-A-is-false-C-B-is-truth-then-if-possible-F-is-truth-or-false-F-A-B-A-C-B-C-

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Question Number 247 by 123456 last updated on 25/Jan/15
A:C is false B:C∨A is false C:B is truth then if possible F is truth or false? F:(A∧B)∨(A∧C)∨(B∧C)
$$\mathrm{A}:\mathrm{C}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{B}:\mathrm{C}\vee\mathrm{A}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{C}:\mathrm{B}\:\mathrm{is}\:\mathrm{truth} \\ $$$$\mathrm{then}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{F}\:\mathrm{is}\:\mathrm{truth}\:\mathrm{or}\:\mathrm{false}? \\ $$$$\mathrm{F}:\left(\mathrm{A}\wedge\mathrm{B}\right)\vee\left(\mathrm{A}\wedge\mathrm{C}\right)\vee\left(\mathrm{B}\wedge\mathrm{C}\right)\: \\ $$
Answered by prakash jain last updated on 17/Dec/14
C∨A=false ⇒ C is false , A is false A∧B is false A∧C is false B∧C is false Hence F is false.
$$\mathrm{C}\vee\mathrm{A}=\mathrm{false}\:\Rightarrow\:\mathrm{C}\:\mathrm{is}\:\mathrm{false}\:,\:\mathrm{A}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{A}\wedge\mathrm{B}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{A}\wedge\mathrm{C}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{B}\wedge\mathrm{C}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{Hence}\:\mathrm{F}\:\mathrm{is}\:\mathrm{false}. \\ $$

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