# Consider :Statement - I : Statement - II : Option 1) Statement - I is false ; Statement - II is true.   Option 2) Statement - I is true ; Statement - II is true ; Statement - II is a correct explanation for Statement - I.     Option 3) Statement - I is true ; Statement - II is true ; Statement - II is not a correct explanation for Statement - I.     Option 4) Statement - I is true ; Statement - II is false.

As learnt in

Truth Table of 'AND' operator -

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Truth table of 'OR' operator -

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Truth Table of "if-then" -

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Truth Table of "if and only if" -

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Tautology -

A statement pattern is called tautalogy, if it is always true, whatever may be the truth values of constitute statements.

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A statement pattern is called a fallacy if it is always false, whatever may be the truth values of its constituent statements.

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 $p$ $q$ $p\wedge \sim q$ $\sim p\wedge q$ $\left ( p\wedge \sim q \right )\wedge \left ( \sim p\wedge q \right )$ $T$ $T$ $F$ $F$ $F$ $T$ $F$ $T$ $F$ $F$ $F$ $T$ $F$ $T$ $F$ $F$ $F$ $F$ $F$ $F$

It is fallacy.

 $p$ $q$ $p\rightarrow q$ $\sim q\rightarrow \sim p$ $\left ( p\rightarrow q \right )\leftrightarrow \left ( \sim q\rightarrow \sim p \right )$ $T$ $T$ $T$ $T$ $T$ $T$ $F$ $F$ $F$ $T$ $F$ $T$ $T$ $T$ $T$ $F$ $F$ $T$ $T$ $T$

It is tautology

Option 1)

Statement - I is false ; Statement - II is true.

Incorrect option

Option 2)

Statement - I is true ; Statement - II is true ; Statement - II is a correct explanation for Statement - I.

Incorrect option

Option 3)

Statement - I is true ; Statement - II is true ; Statement - II is not a correct explanation for Statement - I.

Correct option

Option 4)

Statement - I is true ; Statement - II is false.

Incorrect option

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