Answer
A compound statement is: He can pass if and only if he will study and he can’t pass.
Symbolic form is: \[(p\leftrightarrow q)\wedge \tilde{\ }p\]
Work Step by Step
Let the compound statement be,
“He can pass if and only if he will study and he can’t pass.”
Here, two connectives are ‘if and only if’ and ‘and’.
Simple statements are:
p: He can pass,
q: He will study.
Consider the given compound statement. Use the following representation:
p: He can pass.
q: He will study.
Now, consider the first part.
It contains ‘if and only if’ connective between p and q which can be written as:
\[p\leftrightarrow q\]
Further,
second part is negation of p, connected through ‘and’ connective, which can be written as:
\[\wedge \tilde{\ }p\]
Then, combine the first and second part’s symbolic form to obtain the symbolic form as:
\[(p\leftrightarrow q)\wedge \tilde{\ }p\]
