Question

Let p and q be the 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. a) You do not drive over 65 miles per hour. b) You drive over 65 miles per hour, but you do not geta 1 speeding ticket. c) You will get a speeding ticket if you drive over 65 miles per hour. d) If you do not drive over 65 miles per hour, then you will not get a speeding ticket. e) Driving over 65 miles per hour is sufficient for getting a speeding ticket.
Determine whether each of these conditional statements is true or false. 2 a) If 1+1= 2, then 2 +2 !! en c) If l+I= 3, then 2+2 =5.
Write each of these propositions in the form "p if and only if q" in English. a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside. b) For you to win the contest it is necessary and sufficient that you have the only winning ticket.

Let p, q, and r be the propositions p:Grizzly bears have been seen in the area. q: Hiking is safe on the trail. r: Berries are ripe along the trail. Write these propositions using p, q, and r and logical connectives. a) Berries are ripe along the trail, but grizzly bears have not been seen in the area. b) Grizzły bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail. c) Ifberries are ripe along the trail, hikingg is safe if and only ifgrizzly bears have not been seen in the area. d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.

How many rows appear in a truth table for each of these compound propositions? 5 a) p→-p b) (pv )A(qvs)

Answer 1

1.a)~p

b)p^~q

c)p->q

d)~p->~q

e)p->q

2a). False

Explanation:This biconditonal statement is false because p is true and q is false.

c)True

Explanation:This is a conditional statement. Since p and q are both false, this makes the answer true.

3a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.

Ans:It is hot outside if and only if you buy an ice cream cone.

b)For you to win the contest it is necessary and sufficient that you have the only winning ticket.

Ans:You will win the contest if and only if you have the winning ticket.

4.a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.

Ans:r^~p

Explanation:conjunction of r and negation of p.

b)Grizzły bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.

Ans:~p^q^r

Explanation:Negation of p conjunction of q and conjunction of r.

c) If berries are ripe along the trail, hikingg is safe if and only if grizzly bears have not been seen in the area.

Ans:r->(q<->~p)

Explanation:conditional statement of r and q biconditional of negation of p.

d)It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail
are ripe.

Ans:~q^~p^r

Explanation:Negation of q conjunction of negation p conjunction of r.

5.The number of rows can be obtained by N=2^n where n = the number of propositional variables.

a)p→-p

No.of rows=2^1=2 rows.
b) (pv )A(qvs)

No.of rows=2^3=8 rows.