CSCI 1301

Test 1

Please finish this test and email your answers to the instructor on Blackboard mail. You may use any typeset program (Microsoft Word), or hand-write and then scan/photograph your answers.

- Let
*p*and*q*be the propositions

*p*:Â Â Â Â Â Â Â Â today is a Sunday

*q*:Â Â Â Â Â Â Â Â today is sunny

Write these propositions using *p* and *q *and logical connectives (including negations).

a.)Â Â Â Â Â Â Â Today is not sunny.

b.)Â Â Â Â Â Â Â Today is a sunny Sunday.

c.)Â Â Â Â Â Â Â If today is not sunny, then it is not a Sunday.

This problem is similar to P.13 #13,#14.

- Determine whether each of these conditional statements is true or false.

a.)Â Â Â Â Â Â Â If 1 + 3 = 5, then 2 + 4 = 6.

b.)Â Â Â Â Â Â Â If 1 + 3 > 5, then 2 + 4 > 6.

c.)Â Â Â Â Â Â Â If 1 + 3 < 5, then 2 + 4 < 6.

This problem is similar to P.14 #17.

- Construct a truth table for the compound proposition .

This problem is similar to P.15 #31,#32.

- Use De Morgan’s laws to find the negation of each of the following statements.

a.)Â Â Â Â Â Â Â Today is sunny and today is not a Sunday.

b.)Â Â Â Â Â Â Â Today is not sunny but today is a Sunday.

c.)Â Â Â Â Â Â Â Today is not sunny or today is not a Sunday

This problem is similar to P. 34 #7.

- Let be the statement â€œ
*x*can speak Russianâ€ and be the statement â€œ*x*knows the computer language Câ€. Express each of the following two sentences in terms of quantifiers and logical connectives. The domain for quantifiers consists of all students at your school.

a.)Â Â Â Â Â Â Â Every student at your school can speak Russian and no student at your Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â school knows the computer language C.

b.)Â Â Â Â Â Â Â Every student at your school who can speak Russian does not know the Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â computer language C.

c.)Â Â Â Â Â Â Â No student at your school can both speak Russian and know the computer language C.

This problem is similar to P.53 #9, #10.

- Let be the statement â€œâ€. If the domain consists of all integers, what are the truth values of:

a.)

b.)

c.)

This problem is similar to P.67 #26, #27.

- Determine what rule of inference in P.72 Table 1 is used in the following.

a.)Â Â Â Â Â Â Â Today is a Sunday.

Conclusion: There is a game today or today is a Sunday.

b.)Â Â Â Â Â Â Â Today is not a Sunday.

If there is a game today, then today is a Sunday

Conclusion: There is not a game today.

c.)Â Â Â Â Â Â Â If today is a Sunday, then there is a game today.

If there is a game today, then there is a dinner tomorrow.

Conclusion: If today is a Sunday, then there is a dinner tomorrow.

This problem is similar to P.79 #19.

- Show that a word of six letters must have at least four consonants or at least three vowels.

This problem is similar to P.91 #22, #23.