MA8351 DM - PART A

Which of the following statement is a proposition?

• Get me a glass of milkshake
•  God bless you!
• What is the time now?
• The only odd prime number is 2

Let P: We give a nice overall squad performance, Q: We will win the match.<br />Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance.“ is?

• P v Q
• Q ∧ P
• Q<->P
• ~P v Q

If there are ‘M’ switches in parallel numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary

• 1∧ 2∧ 3 ∧ … ∧M should be on
• 1∧ 2∧ 3 ∧ … ∧M should be off
• 1 v 2 v 3 v … v M should be on
• None of the mentioned

What is the converse of the conditional statement “If it ices today, I will play ice hockey tomorrow.”

• “I will play ice hockey tomorrow only if it ices today.”
• “If I do not play ice hockey tomorrow, then it will not have iced today.”
• “If it does not ice today, then I will not play ice hockey tomorrow.”
• “I will not play ice hockey tomorrow only if it ices today.”

Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”

• ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures
• ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class
• ∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures
• ∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

When to proof P→Q true, we proof P false, that type of proof is known as ___________

• Direct proof
• Contrapositive proofs
• Vacuous proof
• Mathematical Induction

For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________

• (m^2)+3
• m+1
• (m^m)
• 3*(m^2)+4

A polygon with 7 sides can be triangulated into ________

• 7
• 14
• 5
• 10

There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

• 7! * 6
•  7C5
• 7!
• same area

What is the recurrence relation for 1, 7, 31, 127, 499?

• bn+1=5bn-1+3
• bn=4bn+7!
• bn=4bn-1+3
• bn=bn-1+1