Conditional statement
&If you go to the zoo to see a lion,
&then you will see a cat.
This is a true statement, since lions are members of the cat family. This means lions are a subset of cats. With this information we can create the following Venn diagram.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
Converse
&If you see a cat,
&then you have gone to the zoo to see a lion.
This is not a true statement, because you could see a cat that is not a lion outside of the zoo. As explained, lions are a subset of the animal family we call cats.
b Let's write the conditional statement, p→ q.
Conditional statement
&If you play a sport,
&then you wear a helmet.
This is false, because not all sports require helmets. To draw a Venn diagram, think about when we are required to wear a helmet. Some sports require helmets, but it is also required if you are, for example, working construction. Therefore, the circle describing sports should intersect the circle describing activities that requires helmet.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
Converse
&If you wear a helmet,
&then you play a sport.
This is not a true statement because, as previously explained, helmets are not exclusively used when playing sports.
c Let's write the conditional statement, p→ q.
Conditional statement
&If this month has 31 days,
&then it is not February.
This is a true statement, since February has 28 or 29 days, depending on the year. In addition to the month of February, there are two other kinds of months — those with 30 days, and those with 31 days. There is no overlap between these months so we need three separate circles, one for each month when drawing our Venn diagram.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
Converse
&If it is not February,
&then this month has 31 days.
This is not a true statement, because the month could also have 30 days.
