Question

express the following compound statements symbolically without examining in truth values​

Answer 1

(i) Given,

$\longrightarrow\textit{`` 2 is an even number and 25 is a perfect square."}$

This compound statement is broken into its components as follows:

$\longrightarrow\sf{p}:\textit{`` 2 is an even number."}$

$\longrightarrow\sf{q}:\textit{`` 25 is a perfect square."}$

The connective "AND" is used in between them.

Hence the sentence in symbolic form is $\sf{\underline{\underline{p\land q.}}}$

(ii) Given,

$\longrightarrow\textit{``A school is ope\,\!n or there is a holiday."}$

This compound statement is broken into its components as follows:

$\longrightarrow\sf{p}:\textit{``A school is ope\,\!n."}$

$\longrightarrow\sf{q}:\textit{``There is a holiday."}$

The connective "OR" is used in between them.

Hence the sentence in symbolic form is $\sf{\underline{\underline{p\lor q.}}}$

(iii) Given,

$\longrightarrow\textit{``Delhi is in India but Dhaka is not in Srilanka."}$

The statement can be rewritten without changing the meaning as,

$\longrightarrow\textit{``Delhi is in India and Dhaka is not in Srilanka."}$

This compound statement is broken into its components as follows:

$\longrightarrow\sf{p}:\textit{``Delhi is in India."}$

$\longrightarrow\sf{q}:\textit{``Dhaka is not in Srilanka."}$

The connective "AND" is used in between them.

Hence the sentence in symbolic form is $\sf{\underline{\underline{p\land q.}}}$

But if,

$\longrightarrow\sf{q}:\textit{``Dhaka is in Srilanka."}$

then the sentence in symbolic form is $\sf{\underline{\underline{p\land\lnot q.}}}$

(iv) Given,

$\longrightarrow\textit{``\, 3+8\geq12 if and only if 5\times4\leq25. "}$

This compound statement is broken into its components as follows:

$\longrightarrow\sf{p}:\textit{``\, 3+8\geq12. "}$

$\longrightarrow\sf{q}:\textit{``\, 5\times4\leq25. "}$

The connective "IF AND ONLY IF" is used in between them.

Hence the sentence in symbolic form is $\sf{\underline{\underline{p\iff q.}}}$