Recent questions tagged ch14

Consider the statement $ \log \bigg(\large\frac{5c}{a} \bigg),\: \log \bigg(\large\frac{3b}{5c} \bigg)$ and $ \log \bigg(\large\frac{a}{3b} \bigg)$ are in AP, where a,b,c are in GP. The statement is true only if a,b,c are the lengths of sides of

asked Jan 23, 2014 by thanvigandhi_1

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

asked Jan 23, 2014 by thanvigandhi_1

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Which one of the following is a fallacy?

asked Jan 23, 2014 by thanvigandhi_1

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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

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

asked Jan 23, 2014 by thanvigandhi_1

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S1 : The function $f(x)=|x|$ is not one-one.\[\] S2: The negative real numbers are not the images of any real numbers. \[\] If the statement S1 holds true then,

asked Jan 23, 2014 by thanvigandhi_1

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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

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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

Let A and B denote the statements \[ \] A: $ \cos \alpha + \cos \beta + \cos \gamma = 0$ \[\] B: $ \sin \alpha + \sin \beta + \sin \gamma = 0$ \[\] If $ \cos(\beta- \alpha) + \cos( \gamma- \alpha) + \cos( \alpha - \beta)= -\large\frac{3}{2}$, then

asked Jan 22, 2014 by thanvigandhi_1

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For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

asked Jan 22, 2014 by thanvigandhi_1

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The inverse of the converse of a conditional statement is the _______________.

asked Jan 22, 2014 by thanvigandhi_1

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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

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In a class of 50 students, 18 take music, 26 take art, and 2 take both art and music. How many students in the class are not enrolled in either music or art?

asked Jan 22, 2014 by thanvigandhi_1

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Which of the following is not a false statement?

asked Jan 21, 2014 by thanvigandhi_1

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Which of the following is a true statement?

asked Jan 21, 2014 by thanvigandhi_1

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