$$ In the truth table, there are errors in slogan $3$ and slogan $4$ columns. Once you correct these columns, try #$4$ again. Remember you are looking at the columns $($not the rows$).$

Project #$3$

Your boss also specializes as a logician$,$ and he is concerned about various slogans around the office. Reflect on the slogans below and answer the questions using truth tables as discussed in module $04.$

The slogans in question are:

Slogan $1$: $"$If we have bread, peace, and land, then we will not take a step back!"

Slogan $2$: $"$If we do not have bread, peace, and land, then we will not take a step back!"

Slogan $3$: $"$If we do not take a step back, then we will have bread, peace, and land!"

Slogan $4$: $"$If we take a step back, then we will not have bread, peace, and land!"

Break the slogans into two simple statements $($P and Q$).$ Hint: Use the positive form of the statement to avoid confusion. In other words, do not use $$not$$ in your statements.

P $=$ We have bread, peace, and land.

Q $=$ We will take a step back.

Write each of the four slogans in mathematical notation $($symbol format$).$

Slogan $1=$ P $->$ Q

Slogan $2=$ P $->$ Q

Slogan $3=$ Q $->$P

Slogan $4=$ Q $->$ P

Fill out the truth table below. Include the symbol format of each slogan.

Slogan $1$

Slogan $2$

Slogan $3$

Slogan $4$

P Q $$P $$Q P $->$ Q

$$ P $->$ Q $$ Q $->$P Q $->$ P

T T F F F T T F

T F F T T T F T

F T T F T F T F

F F T T T T T T

Compare the last four columns $($the truth values of the slogans$).$ Do any of the columns match exactly? If so$,$ this means that these slogans are logically equivalent. Therefore, can you say any of the slogans are logically equivalent? Explain.