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MTH 221 Wk 3 - Midterm Exam

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MTH 221 Wk 3 - Midterm Exam

Complete the midterm exam. You have one attempt at the exam. So, be sure to review all previous course materials before attempting the exam.

Question 1

The propositional variables s and m represent the two propositions:

 

s: It is sunny today.

 

m: I will bring my umbrella.

 

 

Select the logical expression that represents the statement: "Despite the fact that it is sunny today, I will bring my umbrella."

 

 

s

 

 

s logical and m

 

 

s logical or m

 

 

not m

 

 

Question 2

p = F, q = T, and r = T.

 

Select the expression that evaluates to true.

 

 

not left parenthesis q logical or r right parenthesis

 

 

left parenthesis not p logical and r right parenthesis logical or q

 

 

left parenthesis not q logical or r right parenthesis logical and p

 

 

p logical or not q logical or not r

 

 

Question 3

Select the statement that is false.

 

 

 

If 3 is a prime number, then 5 is a prime number.

 

 

If 4 is a prime number, then 6 is a prime number.

 

 

If 4 is a prime number, then 5 is a prime number.

 

 

If 3 is a prime number, then 6 is a prime number.

 

 

Question 4

 

Use De Morgan’s law to select the statement that is equivalent to:

 

"It is not true that the patient has high blood pressure or influenza."

 

 

The patient has high blood pressure or has influenza.

 

 

The patient does not have high blood pressure and does not have influenza.

 

 

The patient does not have high blood pressure or does not have influenza.

 

 

The patient has high blood pressure and has influenza.

 

 

Question 5

 

Select the law which shows that the two propositions are logically equivalent.

 

 

 

left parenthesis not p logical and left parenthesis r logical or not q right parenthesis right parenthesis logical or left parenthesis not left parenthesis not p logical and w right parenthesis not p logical and left parenthesis left parenthesis r logical or not q right parenthesis logical or w right parenthesis

 

 

 

 

DeMorgan’s law

 

 

Distributive law

 

 

Associative law

 

 

Commutative law

 

 

Question 6

The predicate T is defined as:

 

 

T left parenthesis x comma y comma z right parenthesis colon space left parenthesis x space plus space y right parenthesis squared space equals space z

 

Select the proposition that is true.

 

T(4, 1, 5)

 

 

T(4, 1, 25)

 

 

T(1, 1, 1)

 

 

T(4, 0 2)

 

 

Question 7

The domain of discourse are the students in a class. Define the predicates:

 

S(x): x studied for the test

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