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Recent questions tagged implications-(tautology-contradiction.)

The statement $\sim(p \leftrightarrow \sim q)$ is

asked Apr 6, 2014 by balaji.thirumalai

1 answer

Statement-1: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy, and Statement-2 : $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology. Given these two statements, which of the following is true?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Which of the following are tautologies and which are contradictions?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Choose the correct answer. The statement $p \rightarrow (q \rightarrow p)$ is equivalent to which of the following?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

The proposition $(P \vee Q) \vee (\sim P \wedge \sim Q)$ is a:

asked Mar 20, 2014 by balaji.thirumalai

1 answer

$^{\sim}(p \Rightarrow q)$ is equivalent to

asked Jan 24, 2014 by thanvigandhi_1

1 answer

$ ^{\sim}(p V q)$ is equivalent to

asked Jan 24, 2014 by thanvigandhi_1

1 answer

$ ^{\sim}(p \wedge q)$ is equivalent to

asked Jan 24, 2014 by thanvigandhi_1

1 answer

$ ^{\sim}(p \leftrightarrow q)$ is equivalent to

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$(p \wedge\: ^{\sim}q) \wedge (^{\sim}p V q)$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$ ^{\sim}[(p \wedge q) \rightarrow (^{\sim}p V q)]$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If p,q,r are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true, then

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If p, q, r are simple propositions with truth values T,F,T then the truth value of $ [(^{\sim}p Vq) \wedge ^{\sim}r] \Rightarrow p$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The statement $ p V q \Rightarrow \: p \wedge q$ is a

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The contrapositive of $ (p V q) \Rightarrow r$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If a,b,c are the sides of a triangle, then the statement, “$ \large\frac{1}{(b+c)},\: \large\frac{1}{(c+a)},\: \large\frac{1}{(a+b)}$ are also the sides of the triangle”, is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If p : It rains today. q : I go to school. r : I shall meet my friends. s : I shall go for a movie. Then which of the following is the proportionate representation of the statement, If it does not rain or if I do not go to school, then I shall meet my friends and go for a movie.

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The proposition $ (p \Rightarrow \: ^{\sim}p) \wedge (^{\sim}p \Rightarrow p)$ is a

asked Jan 23, 2014 by thanvigandhi_1

1 answer

Which one of the following is a fallacy?

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If $ \phi(x) = f(x) + f(1-x), f’(x)<0 \: for\: 0 \leq x \leq 1$, then the tautology among the following is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The proposition $ p \Rightarrow ^{\sim}(p \wedge\: ^{\sim}q)$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The first two terms of a geometric progression add up to 12. The terms of the G.P. are alternately positive and negative.The statement - The sum of the third and the fourth terms is 48 holds true for the first term being

asked Jan 23, 2014 by thanvigandhi_1

1 answer

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number” and r be the statement “x is a rational number iff y is a transcendental number”. \[\] S1 : r is equivalent to either q or p \[\] S2 : r is equivalent to $ ^{\sim}(p \leftrightarrow \: ^{\sim}q)$

asked Jan 22, 2014 by thanvigandhi_1

1 answer

S1:$ ^{\sim} (p \leftrightarrow\: ^{\sim} q)$ is equivalent to $p \leftrightarrow q.$ \[\] S2 :$ ^{\sim} (p\leftrightarrow \: ^{\sim} q)$ is a tautology.

asked Jan 22, 2014 by thanvigandhi_1

1 answer

Given : $P(x) =x^4 + ax^3 + bx^2 + cx + d$ such that $x=0$ is the real root of $P'(x)=0$. If $P(-1) < P(1)$, then in the interval $[-1, 1]$, which of the following statement is wrong.

asked Jan 22, 2014 by thanvigandhi_1

1 answer

What is true about the statement "If two angles are right angles, the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?

asked Jan 22, 2014 by thanvigandhi_1

1 answer

Let A={2,3,5,7}. For which of the sets, truth value is true?

asked Jan 21, 2014 by thanvigandhi_1

1 answer

What is the converse of the statement: n is divisible by 3, if the sum of digits of n is divisible by 3?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

What is the contrapositive of the statement: If $f(2)=0$, then $ f(x)$ is divisible by $(x-2)$?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

What is the converse of the statement: If $x-4 = 5$, then $x=9$?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

What is the contradiction of the statement: In $ \Delta ABC,\: if\: AB=AC$, then angles $C=B$?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

Identify the contrapositive of the statement, If 2 is the only even prime number then 6 is divisible by 3.

asked Jan 20, 2014 by thanvigandhi_1

1 answer

Identify the converse of the statement: If x is a prime number then x is even.

asked Jan 20, 2014 by thanvigandhi_1

1 answer

Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

What is the negation of: For every real number $x ,x \gt x+2$?

asked Jan 20, 2014 by thanvigandhi_1

1 answer

If $ t$ and $ c$ denote a tautology and a contradiction respectively, then for any statement $p, p \wedge t$ is equal to

asked Jan 20, 2014 by thanvigandhi_1

1 answer

Identify the quantifier in the sentence There exists a kingdom for every king in India.

asked Jan 17, 2014 by thanvigandhi_1

1 answer

Identify the quantifier in the sentence: There exists a number which is equal to its square.

asked Jan 17, 2014 by thanvigandhi_1

1 answer

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