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Week 2: Practice HW 2: 3.1–3.6 (Homework) MATH 115, section B10, Fall 2018
Instructor: Ethan Smith
Current Score : Due : Monday, September 10 2018 11:59 PM EDTLast Saved : n/a Saving...
The due date for this assignment is past. Your work can be viewed below, but no changes can be made.
Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you
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Request Extension
1. 0.35/0.35 points | Previous AnswersAufExc4 3.6.023.
Use all of the premises in the argument to determine a valid conclusion for the argument.
All multiples of 17 end with a 5.
1547 is a multiple of 17.
∴ 1547 ends with a 5.
2. 0.35/0.35 points | Previous AnswersAufExc4 3.1.503.XP.
Write the sentence in symbolic form. Represent each component of the sentence with the letter indicated in parentheses.
All squares (s) are rectangles (r).
~r
s∧r
s∨r
r↔s
s→r
State whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional.
conjunction
disjunction
negation
conditional
biconditional
,3. 0.35/0.35 points | Previous AnswersAufExc4 3.3.015.
Construct a truth table for the given statement.
(p ∧ ~q) → [~(p ∧ q)]
p q (p ∧ ~q) → [~ (p ∧ q)]
T T T F F T F T T T
T F T T T T T T F F
F T F F F T T F F T
F F F F T T T F F F
4. 0.35/0.35 points | Previous AnswersAufExc4 3.4.024.
Consider the following statement.
If x + 8 = 11, then x = 3.
(a) Write the converse of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
(b) Write the inverse of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
(c) Write the contrapositive of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
, 5. 0.35/0.35 points | Previous AnswersAufExc4 3.4.005.
Write the statement in "If p, then q" form.
He can join the band, if he has the talent to play a keyboard.
If he can join the band, then he as the talent to play a keyboard.
If he does not have the talent to play a keyboard, then he cannot join the
band.
He can join the band and he has the talent to play a keyboard.
If he has the talent to play a keyboard, then he can join the band.
He can join the band if and only if he has the talent to play a keyboard.
6. 0.35/0.35 points | Previous AnswersAufExc4 3.2.039.
Make use of one of De Morgan's laws to write the given statement in an equivalent form.
She did not visit France and she did not visit Italy.
She did not visit France if she did not visit Italy.
She did not visit either France or Italy.
She did not visit France or she did not visit Italy.
She visited France and she visited Italy.
She did not visit France if and only if she did not visit Italy.
7. 0.35/0.35 points | Previous AnswersAufExc4 3.1.010.
Determine whether the sentence is a statement.
x=x+7
The sentence is a statement.
The sentence is not a statement.
Week 2: Practice HW 2: 3.1–3.6 (Homework) MATH 115, section B10, Fall 2018
Instructor: Ethan Smith
Current Score : Due : Monday, September 10 2018 11:59 PM EDTLast Saved : n/a Saving...
The due date for this assignment is past. Your work can be viewed below, but no changes can be made.
Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you
have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key.
Request Extension
1. 0.35/0.35 points | Previous AnswersAufExc4 3.6.023.
Use all of the premises in the argument to determine a valid conclusion for the argument.
All multiples of 17 end with a 5.
1547 is a multiple of 17.
∴ 1547 ends with a 5.
2. 0.35/0.35 points | Previous AnswersAufExc4 3.1.503.XP.
Write the sentence in symbolic form. Represent each component of the sentence with the letter indicated in parentheses.
All squares (s) are rectangles (r).
~r
s∧r
s∨r
r↔s
s→r
State whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional.
conjunction
disjunction
negation
conditional
biconditional
,3. 0.35/0.35 points | Previous AnswersAufExc4 3.3.015.
Construct a truth table for the given statement.
(p ∧ ~q) → [~(p ∧ q)]
p q (p ∧ ~q) → [~ (p ∧ q)]
T T T F F T F T T T
T F T T T T T T F F
F T F F F T T F F T
F F F F T T T F F F
4. 0.35/0.35 points | Previous AnswersAufExc4 3.4.024.
Consider the following statement.
If x + 8 = 11, then x = 3.
(a) Write the converse of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
(b) Write the inverse of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
(c) Write the contrapositive of the given statement.
If x ≠ 3, then x + 8 ≠ 11.
If x = 3, then x + 8 = 11.
If x + 8 ≠ 11, then x ≠ 3.
, 5. 0.35/0.35 points | Previous AnswersAufExc4 3.4.005.
Write the statement in "If p, then q" form.
He can join the band, if he has the talent to play a keyboard.
If he can join the band, then he as the talent to play a keyboard.
If he does not have the talent to play a keyboard, then he cannot join the
band.
He can join the band and he has the talent to play a keyboard.
If he has the talent to play a keyboard, then he can join the band.
He can join the band if and only if he has the talent to play a keyboard.
6. 0.35/0.35 points | Previous AnswersAufExc4 3.2.039.
Make use of one of De Morgan's laws to write the given statement in an equivalent form.
She did not visit France and she did not visit Italy.
She did not visit France if she did not visit Italy.
She did not visit either France or Italy.
She did not visit France or she did not visit Italy.
She visited France and she visited Italy.
She did not visit France if and only if she did not visit Italy.
7. 0.35/0.35 points | Previous AnswersAufExc4 3.1.010.
Determine whether the sentence is a statement.
x=x+7
The sentence is a statement.
The sentence is not a statement.
