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Question Number 173396 by pete last updated on 11/Jul/22

Consider the statements: x: Birds fly y: The sky is blue Which of the following statements can be represented aa x⇔y? (i) When the sky is blue, the birds fly. (ii) Either the bird is flying or the sky is blue. (iii) Birds fly if and only if the sky is blue. (iv) When birds fly, the sky is blue.

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{statements}: \\ $$$${x}:\:\mathrm{Birds}\:\mathrm{fly} \\ $$$${y}:\:\mathrm{The}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue} \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statements}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{represented}\:\mathrm{aa}\:{x}\Leftrightarrow{y}? \\ $$$$\left({i}\right)\:\mathrm{When}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue},\:\mathrm{the}\:\mathrm{birds}\:\mathrm{fly}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Either}\:\mathrm{the}\:\mathrm{bird}\:\mathrm{is}\:\mathrm{flying}\:\mathrm{or}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue}. \\ $$$$\left({iii}\right)\:\mathrm{Birds}\:\mathrm{fly}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue}. \\ $$$$\left({iv}\right)\:\mathrm{When}\:\mathrm{birds}\:\mathrm{fly},\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue}. \\ $$

Answered by cortano1 last updated on 11/Jul/22

(iii)

$$\left({iii}\right) \\ $$

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