Mathematical Reasoning - Online Test

Q1. The negation of the proposition “if a quadrilateral is a square, then it is a rhombus “ is
Answer : Option C
Explaination / Solution:

rules of negation ∼(p→q)≡p∧∼q

Q2. The contrapositive of (p∨q)→r is
Answer : Option D
Explaination / Solution:

the contrapositive of p→q is∼q→∼p

Q3. The contrapositive of p→(∼q→∼r) is
Answer : Option B
Explaination / Solution:

The contrapositive of p→q is ∼q→∼p

Q4. The contrapositive of the statement “ if  then I get first class” is
Answer : Option C
Explaination / Solution:

p:

q:I get first class

the contrapositive of . hence the answer is If I do not get a first class , then 


Q5. If x = 5 and y = - 2 , then x – 2y = 9 . The contrapositive of this proposition is
Answer : Option D
Explaination / Solution:

p: x = 5 and y = - 2 , q : x – 2y = 9

The contrapositive of 

Hence If x – 2y  9 , then x  5 or y  - 2


Q6. “If the figure is a rhombus then the diagonals are perpendicular “. The contrapositive of the above statement is
Answer : Option B
Explaination / Solution:

p: the figure is a rhombus  q: the diagonals  are perpendicular

Contrapositive of 

hence If the diagonals are not perpendicular, then the figure is not a rhombus


Q7. Which of the following statement is a tautology ?
Answer : Option D
Explaination / Solution:



Q8. The statement p→(q→p) is equivalent to
Answer : Option D
Explaination / Solution:


pq



TTTTTT
TFTTTT
FTFTTT
FFTFTT

 

 

 

 

Hence they are equivalent


Q9. The inverse of the proposition (p∧∼q)→r is
Answer : Option A
Explaination / Solution:

         

   Since 


Q10. Logical equivalent proposition to the proposition ∼(p∨q) is
Answer : Option B
Explaination / Solution:

∼(p∨q)≡∼p∧∼q De Morgan's law