# Mathematical Reasoning - Online Test

Q1. Which of the following is a preposition?
Explaination / Solution:

It is a false statement other options are open sentences

Q2. Let p and q be two prepositions given by P : The sky is blue, q : Milk is white, Then , p and q is
Explaination / Solution:

using conjunction to combine statement

Q3. Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p ∧q is
Explaination / Solution:

∧ is replaced by and in verbal form

Q4. Let p and q be two prepositions given by p : It is hot, q : He wants water Then , the verbal meaning of p→q is
Explaination / Solution:

→ symbol is replaced by if p then q

Q5. Let p and q be two prepositions given by p : I take only bread and butter in breakfast. q : I do not take anything in breakfast. Then , the compound proposition “ I take only bread and butter in breakfast or I do not take anything “ is represented by
Explaination / Solution:

and is replaced by ∧ or is replaced by ∨

Q6. Let p and q be two prepositions given by p : I take medicine, q : I can sleep then ,the compound statement ∼p→q means
Explaination / Solution:
No Explaination.

Q7. Let p and q be two prepositions given by p : To become an airforce officer one should be graduate. q : To become an airforce officer one should have good health. The compound proposition “ To become an airforce officer one should be a graduate and should have good health “ is represented by
Explaination / Solution:

the statement before and is p .The statement after and is q.and is replaced by∧

Q8. Let p and q be two prepositions given by p : A parallelogram is a rhombus. q : The diagonals are at right angles. The compound proposition “ A parallelogram is a rhombus iff its diagonals are at right angles “ is represented by
Explaination / Solution:

iff means a double implication statement so symbolic form has ↔

Q9. Let p and q be two prepositions given by p : I have the raincoat, q : I can walk in rain. The compound proposition “ If I have the raincoat , then I can walk in the rain “ is represented by
Explaination / Solution:

If then means an implication statement .hence we rewrite as p→q

Q10. Which of the following is true for the propositions p and q ?
Explaination / Solution:

only F∨F≡F Hence ∼F≡T