A. Determine whether each of the sentences below is a proposition or not.

1. All multiple of 5 are odds.
2. x is a real number.
3. Sketch the graph f.
4. Five is greater than 4.
5. -1<0.
6. The sun is shining.
7. The sum of two prime numbers is even
8. 3 + 4 = 7.
9. It rained in Manila, on October 30 1999.
10. x+y>10

B. State whether or not the following are propositions. In case a proposition, indicate if it is true or false.

1. All perfect squares are even numbers
2. Every decimal number is a rational number.
3. The summation i-100i.
4. Either x is divisible by 3 or it is not.
5. If2x+7=x then x=-7.

C. Construct a truth table for each of these compound statements. Number is already done for you.

1. pqpq

Solution:

p	q	pq	pq	pqpq
T	T	T	T	T
T	F	T	F	F
F	T	T	F	F
F	F	F	F	T

2. pqpq

3. pqpq

4. pqpq

5. pqpr

D. Let p: The election is decided and q: The votes have been counted.

Express each of these compound propositions as an English sentence.

1. p

2.qp

3.pq

4.pq

5.qp

E. Letp, q, and rbe the propositions

p: You get a 95 on the final exam.

q: You do every exercise in the class.

r: You get a 95 in MMW.

Write the propositions in symbols usingp, q, r and logical connectives.

1. You get a 95 in MMW, but you do not do every exercise in the class.
2. You get a 95 on the final examination, you do every exercise in the class and you get 95 in MMW.
3. To get a 95 in MMW, it is necessary for you to get a 95 on the final examination.
4. You get a 95 on the final examination, but you do not do every exercise in the class, nevertheless you get a 95 in MMW.

F. Show that the following statement is a contradiction, a tautology.

1.pq(p)(q)

2.(p(p)