Question

Task Conditional Statements mat Tools Add-ons Help Last edit was yesterday at 7:37 PM ormal text Arial + BIU A E 15 E A. MO ART HOURS Modern Art Museum Monday Tuesday Wednesday Thursday Friday Saturday Sunday Closed 10:00 AM 10:00 AM 10:00 AM 9:00 AM 9:00 AM 12:00 AM 8:00 PM 6:00 PM 8:00 PM 6:00 PM 6:00 PM 5:00 PM a) Write a conditional to describe the hours of the museum on Mondays. b) Write a conditional to describe the hours of the museum on Thursdays. c) Write the converse, inverse, and contrapositive of the conditional of the conditional you wrote in part (b). Then give the truth value for each statement. d) Can each condition you wrote in for parts (a) and (b) be written as a true bi conditional? Why or Why not? If so, give each biconditional.

Answer 1

A conditional statement is an if-then statement in which p is a hypothesis and q is a conclusion.

a)

In this case the hypothesis is: It is monday

The conclusion is: the museum is closed.

Then the conditional statement for the hours of the musuem on mondays is:

If it is monday then the museum is closed.

b)

In this case the hypothesis is: it is thursday

the conclusion is: the museum opens from 10 am to 8 pm.

Then the conditional is:

If it is thursday then the museum opens from 10 am to 8 pm.

c)

To find the converse statement we need to interchange the hypothesis and the conclusion, therefore the converse of b is:

If the museum opens from 10 am to 8 pm then it is thursday.

Since the museum opens in the same hours on tuesday, then this statement is false.

To find the inverse statement we need to negate the hypothesis and conclusion, therefore the inverse of b is:

If it is not thursday then the museum does not open from 10 am to 8pm.

Since the museum opens in this hours on tuesday, then this statement is false.

To find the contrapositive statement we need to interchange the hypothesis and the conclusion of the inverse statement, then the contrapositive of b is:

If the museum does not open from 10 am to 8 pm then it is not thursday.

Since we the museum only opens in this hours two days of the week and one of them is thursday, then this statement is true.

d)

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

With this is mind a true biconditional is a statement in whose conditional and its converse are true.

The statement in part b can't be written as a true biconditional, since the converse is false.

The statement in part a can be express as a biconditional because its converse is true. Then:

It is monday if and only if the museum is closed.