Exam 3: Logic

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -Trevor wanted to attend the meeting, but he had to go to the party.

Construct a truth table for the statement. - $(p \rightarrow q) \rightarrow(\sim p \vee q)$

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ At most, 100 guests arrived at the wedding reception. $\mathrm{q}=$ There was a lot of cake left over. It is not the case that, at most, 100 guests arrived at the wedding reception and there was a lot of cake left over.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -It is not the case that Jim does not play football and Michael does not play basketball.

Construct a truth table for the statement. - $(r \wedge p) \wedge(\sim p \vee t)$

Construct a truth table for the statement. - $(P \wedge \sim t) \wedge s$

Write a negation of the statement. -She earns more than me.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $( p \wedge \sim q ) \wedge \mathbf { r }$

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. -If a is not an even counting number, then the product of a and the counting number b is not an Even counting number.

Identify the standard form of the argument. - \rightarrow \therefore

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -I?ll exercise if I eat too much.

Construct a truth table for the statement. - $\sim((w \wedge t) \vee q)$

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $\sim p \vee ( \sim p \rightarrow \sim q )$

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -It is not true that if you take your vitamins you will stay healthy.

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $\sim ( p \wedge q ) , \sim p \vee q$

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -0 > -4 and 8 ≤ 10

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ The cab is late. $\mathrm{q}$ = The plane takes off on time. $\mathrm{r}=$ Nancy has her plane ticket. The cab is late or the plane does not take off on time, and Nancy does not have her ticke

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -0 > -4 or 2 ≤ 10

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football or Michael plays basketball.

Write the indicated statement. Use De Morgan's Laws if necessary. -If it is love, then it is blind. Contrapositive