Homework 2 1) a. Write 2 simple statements and 3 compound statements in sentence form. For the compound statements, use a different connective for each. You need to have a negation in at least one of...

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Homework 2 1) a. Write 2 simple statements and 3 compound statements in sentence form. For the compound statements, use a different connective for each. You need to have a negation in at least one of your compound statements. Underline the connectives. b. Write your 3 compound statements symbolically. c. Write truth tables for your three compound statements. 2) Construct a truth table for the following statements: a. ~q → p b. (p ∧ q) → (q ∧ p) c. r ↔ (p ∨ ~q) 3) How many lines would a truth table for the following statement contain? For bonus points, construct the truth table. (~p ∧ ~q) → (s → r) 4) Let p be “it is raining”, q be “I will go outside”, r be “I will bring an umbrella” and s be “I will get wet”. Translate the following sentences into symbolic logic: a. If it is not raining, I will go outside. b. It is raining and I will bring an umbrella or I will get wet. c. If it is raining, I will go outside and if I bring an umbrella, I will not get wet. d. If and only if it is raining, I will get wet if I go outside and do not bring an umbrella 5) Show that the following pairs of statements are equal to each other using truth tables. a. p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r) b. p → q = ~q → ~p 6) Bonus: Create 4 statements in the mold of the statements in number 4. The statements should be at least somewhat related. Write 4 sentences using these statements, translate these sentences into symbolic logic and write truth tables for the four.
Answered 7 days AfterJun 07, 2021

Answer To: Homework 2 1) a. Write 2 simple statements and 3 compound statements in sentence form. For the...

Dr. Shikha Maheshwari answered on Jun 14 2021
139 Votes
Homework 2
1) a. Write 2 simple statements and 3 compound statements in sentence form. For the compound
statements, use a different connective for e
ach. You need to have a negation in at least one of
your compound statements. Underline the connectives.
b. Write your 3 compound statements symbolically.
c. Write truth tables for your three compound statements.
Sol.
a. 2 simple statements in sentence form are as follows
(i) No rectangles are square.
(ii) There will be snow in January.
3 compound statements in sentence form are as follows
(i) Daksh is honest or unhealthy.
(ii) Daksh is not honest and healthy.
(iii) Daksh is unhealthy or Daksh is both honest and healthy.
b. Let p be the statement “Daksh is honest” and Let q be the statement “Daksh is healthy”
The symbolical representation of above 3 compound statements are as follows
(i) p∨ ~q
(ii) ~p ∧ q
(iii) ~q ∨ (p∧ q)
c. The truth tables for above three compound statements p∨ ~q, p ∧ q and ~q ∨ (p∧ q) are as
follows
p q ~p ~q p∨ ~q

~p ∧ q

p∧ q ~q ∨
(p∧ q)
T T F F T F T T
T F F T T F F T
F T T F F T F F
F F T T T F F T
2) Construct a truth table for the following statements:
a. ~q → p
b. (p ∧ q) → (q ∧ p)
c. r ↔ (p ∨ ~q)
Sol. The truth table of the given statements are as follows:
a. ~q → p
p q ~q ~q → p

T T F T
T F T T
F T F T
F F T F
b. (p ∧ q) → (q ∧ p)
p q p ∧ q q ∧ p (p ∧ q) → (q ∧ p)

T T T T T
T F F F T
F T F F T
F F F F T
c. r ↔ (p ∨ ~q)
p q r ~q p ∨ ~q r ↔ (p ∨...
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