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Maths Survey
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Maths Survey
Question No: 01
Write the statement in symbolic form:
P= the chilly is spicy
Q= the sour cream is cold
It is false that if the sour cream is not cold then the chilly is spicy
Symbolic form: ~q p = false
Question No: 02
Write the statement in symbolic form
q= the temperature is 90 degree
p= the air conditioner is working
r= the apartment is working
If the air conditioner is working then the temperature is 90 degrees, if and only if the apartment is hot
Symbolic form: qp r
Question No: 03
Write the statement in symbolic form and create the truth table
I am hungry, and I want to eat healthy lunch and I want to eat in hurry
Symbolic Form: p ^ q ^ r
Truth Table:
p
q
r
p ^ q ^ r
T
T
T
T
F
T
T
F
T
F
T
F
F
F
T
F
T
T
F
F
F
T
F
F
T
F
F
F
F
F
F
F
Question No: 04
Determine the truth value of the statement if p is true, q is false, and r is true
~p ^ (~q v ~r)
p
q
r
~p
~q
~r
(~q v ~r)
~p ^ (~q v ~r)
T
F
T
F
T
F
T
F
Question No: 05
Construct a truth table for
(p ^q) (q v r)
p
q
r
p ^ r
q v r
(p ^q) (q v r)
T
T
T
T
T
T
F
T
T
F
T
F
T
F
T
T
T
T
F
F
T
F
T
F
T
T
F
T
T
F
F
T
F
F
T
F
T
F
F
F
F
T
F
F
F
F
F
T
Question No: 06
If p is true, q is false, and r is true then truth value of the statement
r (~p~q)
p
q
r
~p
~q
~r
~p~q
r (~p~q)
T
F
F
F
T
T
F
T
Question No: 07
If Joanne goes to sabre games, then she will not got to Bill games.
If Joanne goes to sabre games = p
She will not go to Bill games = ~q
p~q
Equivalent form:
If Joanne will not go to Bill games = ~p
She will go to sabre games = q
~p ^ q
Question No: 08
Write the contrapositive of the statement
If the quadrilateral is a parallelogram then the opposite sides are parallel
Quadrilateral is a parallelogram = p = true
Opposite sides are parallel = q = true
p q
Contrapositive:
If the quadrilateral is not a parallelogram then the opposite sides are not parallel
Quadrilateral is a not parallelogram = ~p = true
Opposite sides are not parallel = ~q = true
~p~q
Question No: 09
You solve the NewYork Time crosswords puzzle= p
You are genius= q
If you solve the New York Times crossword puzzle then you are genius = pq
You are not genius = ~q
Therefore, you did not solve the New York Times cross word puzzle = ~p
Symbolic form:
((pq) ^ ~q) ~p
Truth Table
p
q
~p
~q
pq
((pq) ^ ~q)
((pq) ^ ~q) ~p
T
T
F
F
T
F
T
T
F
F
T
F
F
T
F
T
T
F
F
F
F
F
F
T
T
T
T
T
The argument is invalid
Question No: 10
Engineering courses are difficult= p
Chemistry labs are long= q
Arts test are easy =r
The engineering courses are difficult and chemistry labs are long = p ^q
If chemistry tests are long then arts tests are easy = pr
Therefore, the engineering courses are difficult and arts tests are not easy = p ^ ~r
Symbolic form:
((P ^ q) ^ pq) p ^ ~r
p
q
r
~p
~q
~r
p ^q
pr
p ^ ~r
((P ^ q) ^ pq) p ^ ~r
T
T
T
F
F
F
T
T
F
F
T
T
F
F
F
T
T
F
T
F
T
F
T
F
T
F
F
T
F
F
T
F
F
F
T
T
F
F
T
F
F
T
T
T
F
F
F
F
F
F
F
T
F
T
F
T
F
T
F
F
F
F
T
T
T
F
F
F
F
F
F
F
F
T
T
T
F
T
F
F
The argument is not valid
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