Decide whether a statement pattern is a tautology, contradiction or contingency

1. A.
   $p\wedge\sim p$
2. B.
   $p\vee\sim p$
3. C.
   $p\vee q$
4. D.
   $(p\wedge(p\to q))\to q$

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1. A.
   a fallacy.
2. B.
   equivalent to $(\sim p)\to q$.
3. C.
   equivalent to $p\to(\sim q)$.
4. D.
   a tautology.

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1. A.
   equivalent to $p \leftrightarrow q$
2. B.
   contingency
3. C.
   tautology
4. D.
   contradiction

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1. A.
   a tautology.
2. B.
   a contingency
3. C.
   a contradiction
4. D.
   equivalent to $p \land q$

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1. A.
   $( \sim q \land p) \land (p \land \sim p)$
2. B.
   $\ (p \land q) \land ( - p \land q)$
3. C.
   $\lbrack( - q) \land p\rbrack \land q$
4. D.
   $( - q \land p) \vee (p \vee \sim p)$

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1. A.
   A and B are contradictions, C and D are tautologies.
2. B.
   A and B are tautologies, C and D are contradictions.
3. C.
   A, B, C, D all are tautologies.
4. D.
   A, B, C, D all are contradictions.

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1. A.
   a contradiction
2. B.
   a tautology
3. C.
   equivalent to $(p \wedge q) \vee r$.
4. D.
   equivalent to $(p \vee q)$ .

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1. A.
   $[(p \to q) \wedge \sim q] \to \sim p$
2. B.
   $(p \to q) \wedge (p \wedge \sim q)$
3. C.
   $[(p \vee q) \wedge \sim p] \wedge \sim q$
4. D.
   $[(p \vee \sim q) \vee (\sim p \wedge q)] \wedge r$

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1. A.
   Result 1 is true, Result 2 is true
2. B.
   Result 1 is true, Result 2 is false
3. C.
   Result 1 is false, Result 2 is true
4. D.
   Result 1 is false, Result 2 is false

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