True or false? "Mozart is a great composer" is a proposition. - ANS fasle - 0pinion
What is the correct meaning of the logical expression p→q∨r∧s ?
a. ((p→q)∨r)∧s
b. (p→(q∨r))∧s
c. p→(q∨(r∧s))
d. p→((q∨r)∧s) - ANS c
Consider the two...
True or false? "Mozart is a great composer" is a proposition. - ANS fasle - 0pinion
What is the correct meaning of the logical expression p→q∨r∧s ?
a. ((p→q)∨r)∧s
b. (p→(q∨r))∧s
c. p→(q∨(r∧s))
d. p→((q∨r)∧s) - ANS c
Consider the two statements:
1. (p → q) ∨ (p → ¬q)
2. (p → q) ∨ (¬p → q).
a. Neither is a tautology.
b. 2. is a tautology, 1. is not.
c. They are both tautologies.
d. 1. is a tautology, 2. is not. - ANS c
1. is a tautology because q true makes (p → q) true and q false makes (p → ¬q) true, regardless
of the truth value of p. Thus (p → q) ∨ (p → ¬q) is always true.
2. is a tautology because p false makes (p → q) true, and p true makes (¬p → q) true,
regardless of the truth value of q. Thus (p → q) ∨ (¬p → q) is always true.
Consider the two statements
1. (p → q) ∧ (p → ¬q)
,2. (p → q) ∧ (¬p → q).
a. neither is a contradiction.
b. 2. is a contradiction, 1. is not.
c. They are both contradictions.
d. 1. is a contradiction, 2. is not. - ANS a
You can see that 1 is not a contradiction because p false makes it true.
You can see that 2 is not a contradiction because q true makes it true.
Identify the converse, inverse and contrapositive of:
If it's a square, then it is a rectangle.
Converse: - ANS Converse: If its a rectangle, then it's a square.
Identify the converse, inverse and contrapositive of:
If it's a square, then it is a rectangle.
Inverse: - ANS If its not a square, then its not a rectangle.
Identify the converse, inverse and contrapositive of:
If it's a square, then it is a rectangle.
Contrapositive: - ANS If it's a not a rectangle, then its not a square.
True or false? The two statements
(p ∧ q) → r
and
(p → r) ∨ (q → r)
are logically equivalent. - ANS True
Select which one of the following statements is logically equivalent to (p → q) → r:
, a. (p ∧ q) ∨ ¬r
b. (p ∧ q) ∨ r
c. (p ∧ ¬q) ∨ r
d. (¬p ∧ q) ∨ r - ANS c
Given real numbers x and y, find the inverse of
x > 0 ∧ y ≥ 0 → x + y > 0.
a. x < 0 ∧ y ≤ 0 → x + y < 0
b. ¬x > 0 ∧ ¬y ≥ 0 → ¬x + ¬y > 0
c. x ≤ 0 ∨ y < 0 → x + y ≤ 0
d. x ≤ 0 ∧ y < 0 → x + y ≤ 0
e. x < 0 ∨ y ≤ 0 → x + y < 0 - ANS c
What is the negation of "Chris has a cat or a dog"?
a. Chris has neither cat nor dog.
b. Chris doesn't have a pet.
c. Chris doesn't have a cat, or Chris doesn't have a dog.
d. Chris has a cat but not a dog, or Chris has a dog but not a cat. - ANS a
True or false? "Having money is a necessary condition for happiness" means that having money
guarantees happiness. - ANS false
"Having money is a necessary condition for happiness" does not mean that having money
guarantees happiness. It means that having money is a precondition for happiness. It is saying
that if you are happy, then you must have money.
True or false? "Absence of evidence of illness is necessary for a clean bill of health from a
doctor" means that if you have no evidence of illness, a doctor will give you a clean bill of health.
- ANS false
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