Answer
The provided statement is neither a tautology nor a self-contradiction.
Work Step by Step
A conjunction \[\wedge \] is true only when both simple statements are true. Similarly, a disjunction\[\vee \] is false only when both component statements are false.
The given compound statement is\[\left( p\wedge q \right)\to \left( \sim q\vee r \right)\], can be first deduced by finding the negation of \[q\]as\[\sim q\].
The negation of a statement can be obtained from complementing the result of that statement.
Then, find\[p\wedge q\]by taking AND combination of two ingredient variables.
Now, find\[\left( \sim q\vee r \right)\]by taking OR combination of two ingredient variables.
Then at last,find\[\left( p\wedge q \right)\to \left( \sim q\vee r \right)\].It is a conditional statement, which would mean that it is false only when the former statement is true, and the latter statement is false. In all other cases, it is true.
To construct the truth table, draw the table having 5 rows and 7 columns in which the elements of the first row are\[p,q,\sim q,\left( p\wedge q \right),\left( \sim q\vee r \right),\left( p\wedge q \right)\to \left( \sim q\vee r \right)\].
The final output is obtained as follows:
