If p and q are true and r and s are false statement then find the truth value of following statements...
1.  (p or s) biconditional(q and r)
2.  ~(p and ~r) and (~q or s).
?

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$$\begin{gathered} \mathbf{A}\mathbf{ }\mathbf{or}\mathbf{ }\mathbf{B}\mathbf{ }\mathbf{it}\mathbf{ }\mathbf{true}\mathbf{ }\mathbf{if}\mathbf{ }\mathbf{one}\mathbf{ }\mathbf{or}\mathbf{ }\mathbf{both}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{A}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{B}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{true}\mathbf{.} \\ \mathbf{A}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{B}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{true}\mathbf{ }\mathbf{if}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{only}\mathbf{ }\mathbf{if}\mathbf{ }\mathbf{both}\mathbf{ }\mathbf{A}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{B}\mathbf{ }\mathbf{are}\mathbf{ }\mathbf{true}\mathbf{.} \\ \mathrm{Now} \\ \mathrm{p} \mathrm{and} \mathrm{q} \mathrm{are} \mathrm{true} \mathrm{and} \mathrm{r} \mathrm{and} \mathrm{s} \mathrm{are} \mathrm{false}. \\ 1. \left(\mathrm{p} \mathrm{or} \mathrm{s}\right)\leftrightarrow \left(\mathrm{q} \mathrm{and} \mathrm{r}\right) \\ \mathrm{p} \mathrm{or} \mathrm{s} \mathrm{is} \mathrm{true} \mathrm{as} \mathrm{p} \mathrm{is} \mathrm{true} \\ \mathrm{q} \mathrm{and} \mathrm{r} \mathrm{is} \mathrm{false} \mathrm{as} \mathrm{r} \mathrm{is} \mathrm{false}. \\ \mathrm{One} \mathrm{compund} \mathrm{statement} \mathrm{is} \mathrm{false} \mathrm{while} \mathrm{other} \mathrm{is} \mathrm{true}. \mathrm{Hence} \mathrm{biconditiontal} \mathrm{statement} \\ \mathrm{is} \mathrm{false}. \\ \Rightarrow \left(\mathrm{p} \mathrm{or} \mathrm{s}\right)\leftrightarrow \left(\mathrm{q} \mathrm{and} \mathrm{r}\right) \mathrm{is} \mathrm{False} \\ 2. ~\left(\mathrm{p} \mathrm{and} ~\mathrm{r}\right) \mathrm{and} \left(~\mathrm{q} \mathrm{or} \mathrm{s}\right) \\ \mathrm{As} \mathrm{r} \mathrm{is} \mathrm{false} \mathrm{hence} \mathrm{negation} \mathrm{of} \mathrm{r} \mathrm{i}.\mathrm{e}. ~\mathrm{r} \mathrm{will} \mathrm{be} \mathrm{true}. \\ \mathrm{Hence} \left(\mathrm{p} \mathrm{and} ~\mathrm{r}\right) \mathrm{is} \mathrm{true} \mathrm{as} \mathrm{both} \mathrm{are} \mathrm{true}. \\ \Rightarrow ~\left(\mathrm{p} \mathrm{and} ~\mathrm{r}\right) \mathrm{is} \mathrm{false}. \\ \mathrm{q} \mathrm{is} \mathrm{true}. \mathrm{Hence} ~\mathrm{q} \mathrm{is} \mathrm{false}. \\ \Rightarrow \left(~\mathrm{q} \mathrm{or} \mathrm{s}\right) \mathrm{is} \mathrm{false} \mathrm{as} \mathrm{both} \mathrm{false}. \\ ~\left(\mathrm{p} \mathrm{and} ~\mathrm{r}\right) \mathrm{and} \left(~\mathrm{q} \mathrm{or} \mathrm{s}\right) \mathrm{is} \mathrm{false} \mathrm{as} \mathrm{both} \mathrm{statements} \mathrm{are} \mathrm{false}. \end{gathered}$$

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