Download ASSIGNMENT QUESTIONS UNIT 3 Fundamentals of Logic contd 1

ASSIGNMENT QUESTIONS
UNIT 3
Fundamentals of Logic contd
1) For the universe of all people, find whether the following is a valid statement:
All mathematics professors have studied calculus
Ramanujan is a mathematics professor
Therefore Ramanujan has studied calculus.
2) Define the Rule of Universal specification and the Rule of Universal Generalization.
3) Prove that for all real numbers x and y, if x + y > 100, then x > 50 or y > 50.
4) Determine if the argument is valid or not. All people concerned about the environment,
recycle their plastic containers. B is not concerned about the environment. Therefore, B
does not recycle his plastic containers.
5) Prove that for every integer n, n2 is even if and only if n is even.
6) Let p(x): x2-7x+10=0,
q(x): x2-2x-3=0,
r(x): x<0.
Determine the truth or falsity of the following statements when the Universe U contains
only the integers 2 and 5.If a statement is false, provide a counterexample.
i) ∀x, p(x)  q(x)
ii) ∃x, q(x)  r(x)
iii) ∃x, p(x)  r(x)
7) Write down the following proposition in symbolic form and find its negation:
“All integers are rational numbers and some rational numbers are not integers”
8) Give i) a direct proof, ii) an indirect proof and iii) proof by contradiction
for the following statement:
“If n is an odd integer, then n+9 is an even integer”
9) Consider the following argument:
I will get grade A in this course or I will not graduate.
If I do not graduate, I will join the army.
I got grade A
I will not join the army.
Is this a valid argument?
10) Write about the Methods of Proof and Disproof for the Conditional.