Tautologies and Fallacies

It is a propositional statement which is always true.

• argument

• fallacy

• logical equivalence

• tautology

It is a propositional statement which is always false.

• argument

• fallacy

• logical equivalence

• tautology

Which of the following statements is a fallacy?

• Today is Wednesday, and tomorrow is not Wednesday.

• If today is raining, then tomorrow is sunny day.

• Today is cloudy or today is windy.

• Today is windy if and only if it is cloudy.

Which of the following is a tautology?

• $\left[\left(p\rightarrow q\right)\wedge\sim q\right]\rightarrow\sim p$

• $\left[\left(p\rightarrow q\right)\wedge q\right]\rightarrow\sim p$

• $\left[\left(p\rightarrow q\right)\wedge\sim q\right]\rightarrow p$

• $\left[\left(p\rightarrow q\right)\wedge q\right]\rightarrow p$

Which of the following propositions is a tautology?

• It is raining or it is not both cold and raining.

• It is raining or it is cold and raining.

• It is raining and it is not cold or raining.

• It is cold and it is raining

Which of the following statements is represented by the logical symbol of the tautology $p\wedge\sim\left(p\vee q\right)$ ?

• Lhea likes cooking but she does not like cooking and washing clothes.

• Lhea either likes cooking but she does not like cooking or washing clothes.

• Lhea likes neither cooking nor she does not like cooking and washing clothes.

• Lhea likes cooking but she does not like either cooking or washing clothes.

Which of the following is a fallacy?

• $p\vee\sim\left(p\vee q\right)$

• $p\wedge\sim\left(p\vee q\right)$

• $\sim p\wedge\left(p\wedge q\right)$

• $p\wedge\left(p\wedge q\right)$

If Mariz enjoys both dancing and singing, then she enjoys dancing.

Which of the following truth tables will prove that the given proposition is a tautology?

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Jane will go to church and it is not possible that if she goes to the mall, then she will go to church.

Which of the following will be the truth table of the given fallacy?

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Which of the following is the corresponding truth table for the proposition 

 $\left(p\rightarrow q\right)\vee\left(p\vee q\right)$ ?

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