COT 3541 Logic For Comp SCI Final
Alt With All Solutions Correct
Which of the following sentences are propositions? Select all that apple.
On your mark, get set, go
(1+2+3)/2 = 3
sin(pi) + cos(pi) < 0.5
Be Quiet! - Ans--(1+2+3)/2 = 3
sin(pi) + cos(pi) < 0.5
Let q, r, and s be propositional variables. Which of the following expressions
are well-defined formulas of propositional logic? Select all the apply.
~~r
--> q
~r~s v r
s v s v r - Ans--~~r
svsvr
Consider the propositions
p: John studies Logic
q: John understands propositional calculus
(a) John doesn't study Logic ___1___
(b) John studies logic or John understands calculus p ____2____
___3_____
(c) John studies Logic and John understands propositional calculus
___4___ ___5____ ___6____
(d) If john studies Logic then john understands propositional calculus
___7___ ___8___ ___9___ - Ans--(a) John doesn't study Logic ___~p___
(b) John studies logic or John understands calculus p ____v____
___q_____
(c) John studies Logic and John understands propositional calculus
___p___ ___^____ ___q____
, (d) If john studies Logic then john understands propositional calculus
___p___ ___-->___ ___q___
Determine whether the given conditional statements are T or F.
(a) If 2 + 2 = 5 then 2/0 = 2 ______
(b) If 2 + 2 = 5 then 4 is an even number _______ - Ans--T
T
The order of operations in the formula p v q ^ r --> q is the same as in ______
((p v q) ^ r) --> q
p v (q ^ (r --> q))
(p v (q ^ r)) --> q
(p v q) ^ (r --> q) - Ans--(p v (q ^ r)) --> q
The number of interpretations of a formula with 7 propositional variables is
______. - Ans--128 (2^7)
Which formulas are tautologies?
p ^ T <-> p
~(p --> ~q)
~~p <-> p
(~p ^(p v q)) --> q - Ans--p ^ T <-> p
~~p <-> p
(~p ^(p v q)) --> q
Let p, q, and r be propositional variables. Which formulas are satisfiable?
Select all that apply.
(~p v q)^(p v ~q)
p ^ ~q ^ ~p ^ q
(p v ~r) ^ (~p v q v r) ^ (~p v ~q)
p v ~q v ~p v q - Ans--(~p v q)^(p v ~q)
(p v ~r) ^ (~p v q v r) ^ (~p v ~q)
p v ~q v ~p v q
From the given list, select all formulas that are logically equivalent to ~p v q.
p<->q
~p --> q
p --> q
Alt With All Solutions Correct
Which of the following sentences are propositions? Select all that apple.
On your mark, get set, go
(1+2+3)/2 = 3
sin(pi) + cos(pi) < 0.5
Be Quiet! - Ans--(1+2+3)/2 = 3
sin(pi) + cos(pi) < 0.5
Let q, r, and s be propositional variables. Which of the following expressions
are well-defined formulas of propositional logic? Select all the apply.
~~r
--> q
~r~s v r
s v s v r - Ans--~~r
svsvr
Consider the propositions
p: John studies Logic
q: John understands propositional calculus
(a) John doesn't study Logic ___1___
(b) John studies logic or John understands calculus p ____2____
___3_____
(c) John studies Logic and John understands propositional calculus
___4___ ___5____ ___6____
(d) If john studies Logic then john understands propositional calculus
___7___ ___8___ ___9___ - Ans--(a) John doesn't study Logic ___~p___
(b) John studies logic or John understands calculus p ____v____
___q_____
(c) John studies Logic and John understands propositional calculus
___p___ ___^____ ___q____
, (d) If john studies Logic then john understands propositional calculus
___p___ ___-->___ ___q___
Determine whether the given conditional statements are T or F.
(a) If 2 + 2 = 5 then 2/0 = 2 ______
(b) If 2 + 2 = 5 then 4 is an even number _______ - Ans--T
T
The order of operations in the formula p v q ^ r --> q is the same as in ______
((p v q) ^ r) --> q
p v (q ^ (r --> q))
(p v (q ^ r)) --> q
(p v q) ^ (r --> q) - Ans--(p v (q ^ r)) --> q
The number of interpretations of a formula with 7 propositional variables is
______. - Ans--128 (2^7)
Which formulas are tautologies?
p ^ T <-> p
~(p --> ~q)
~~p <-> p
(~p ^(p v q)) --> q - Ans--p ^ T <-> p
~~p <-> p
(~p ^(p v q)) --> q
Let p, q, and r be propositional variables. Which formulas are satisfiable?
Select all that apply.
(~p v q)^(p v ~q)
p ^ ~q ^ ~p ^ q
(p v ~r) ^ (~p v q v r) ^ (~p v ~q)
p v ~q v ~p v q - Ans--(~p v q)^(p v ~q)
(p v ~r) ^ (~p v q v r) ^ (~p v ~q)
p v ~q v ~p v q
From the given list, select all formulas that are logically equivalent to ~p v q.
p<->q
~p --> q
p --> q
