Operations and Truth Values of Propositions

The ________________ of two statements is true only if each component is true.

• conjunction

• conditional

• disjunction

• negation

It shows the truthfulness or falsity of a statement.

• conjunction

• conditional

• truth table

• disjunction

The ________________________ of two statements is false only if each component is false.

• conjunction

• conditional

• disjunction

• negation

If  $p$ is false, what is the truth value of  $\sim p$ ?

• true

• false

• cannot be determined

• not enough information

If $p$  is true and  $q$  is false, what is the truth value of  $p∧q$ ?

• false

• true

• cannot be determined

• not enough information

If $p$ is true and  $q$  is false, what is the truth value of  $p\vee q$ ?

• true

• false

• cannot be determined

• not enough information

If  $p$ is true and  $q$ is false, what is the truth value of  $p∧∼q$ ?

• true

• false

• cannot be determined

• not enough information

Which of the following is the correct truth table of  $p∧∼q$ ?

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Which of the following is the correct truth table of the proposition below?
It is both snowing and raining, or it is snowing.
 $p$ : It is snowing.
 $q$ : It is raining.

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Which of the following is the correct truth table of the proposition below?
Either it’s raining, or it’s both snowing and raining.
 $p:$ It is snowing.
 $q:$ It is raining.

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