Answer to Question #165976 in Discrete Mathematics for Angelica Marie Regalado

Question

1. Determine whether each of the following statements is a proposition or not. If it is, give its truth value.

• p: Mindanao is an island in the Philippines. 
• q: Find a number which divides your age. 
• r: My seatmate will get a perfect score in the Logic exam.
• s: Welcome to the Philippines!

1. Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.

• You do not drive over 65 miles per hour.
• You will get a speeding ticket if you drive over 65 miles per hour.
• If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

Answer 1

(1).

p: Mindanao is an island in the Philippines. 

As Mindanano is an island in philippines So given statement is true.

p is true.

q: Find a number which divides your age.

Since we can find the number Which divides my age so

q is true.

r: My seatmate will get a perfect score in the Logic exam.

The given statement has a posibility Whether he will score or not

Whichis either true or false, So It is not a statement.

r is not a statement.

s: Welcome to the Philippines!

Given statement can't decide as true or false.

s is not a statement.

(2). p: You drive over 65 miles per hour. 

q: You get a speeding ticket.

• You do not drive over 65 miles per hour.

~ $p$

• You will get a speeding ticket if you drive over 65 miles per hour.

$p\rightarrow q$

• If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

~$p\rightarrow$ ~$q$