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Math110- Test 2 Review Questions And 100% Correct Answers
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Math110- Test 2 Review Questions And 100%Correct Answers
Determine, for the given truth values of p, q and r, whether the compound proposition is
true or false. Suppose that p is false, q is true, and r is false.
p ∨ (~q ∨ r) - Answer False
Determine for the given truth values of p, q and r whether the compound proposition is
true or false. Suppose p is true, q is true, and r is false.
[~(p ∧ ~q) ∨ r] ∧ (p ∨ ~r) - Answer True
Indicate whether the given compound statement is true or false. Assume that p is a false
statement, q is a true statement, and r is a true statement.
(~p ∧ q) ∧ [(p ∨ ~q) ∧ r] - Answer False
Use one of De Morgan's laws to write an equivalent compound statement.
It is not true that, she received a promotion or that she received a raise.
A: She didn't get promoted and she didn't get a raise.
B: She got promoted but she did not get a raise.
C: She either got promoted or she got a raise, but not both.
D: She got promoted and she got a raise.
E: She did not get a promotion but she did get a raise - Answer A: She did not get a
promotion and she did not get a raise.
Explain why the statement 6 ≤ 8 is a disjunction.
A The symbol ≤ separates, that is, disjoins, the two values.
B The symbol ≤ means "less than and equal to."
, C The symbol ≤ contains the verb of the mathematical statement.
D: The symbol ≤ means "less than or equal to."
E: The symbol = would be a conjunction; anything else is a disjunction. - Answer D: The
symbol ≤ means "less than or equal to."
Determine the truth value of the given statement.
If all frogs can dance, then today is Monday. - Answer True
Determine the truth value of the given statement.
If |x| = 4, then x = 4. - Answer False
Determine whether the given biconditional is true or false. Let x and y be real numbers.
x2 = 49 if and only if x = 7. - Answer False
Determine whether the given biconditional is true or false.
5 = 1 if and only if 6 = 8. - Answer True
Write the sentence in symbolic form. Use v, p, and t as defined below.
v: "I will take a vacation."
p: "I get the promotion."
t: "I will be transferred."
If I am transferred, then I will not take a vacation.
A: v → t
B: t → v
C: ~v → t
D: t → ~v - Answer D: t → ~v
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