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For the following questions answer them individually
If p, q are statements, then $$(\sim p) \vee (\sim q)$$ is equivalent to
If p, q are any two statements, then $$\sim (p \vee (\sim p \wedge q))$$ is equivalent to
If A is the set of all primes not exceeding 20 and is the set of odd positive integers not exceeding 20, then $$(A - B) \cup (B - A) =$$
If $$f(x) = \log \frac{1 + x}{1 - x}$$ and $$g(x) = \frac{3x + x^3}{1 + 3x^2}$$, then f(g(x)) =
If a set A has 4 elements, another set Bhas 7 elements, then the number of injective mappings from into B is
The equation of the line passing through (-4, 3) and is perpendicular to the line segment joining the points (1, -3) and (-5, 1) is
The equation of aline passing through the point (2, 3) and making intercepts in the ratio of 2 : 3 on the x and y axes is
$$\sin^2 \frac{\pi}{4} + \sin^2 \frac{3 \pi}{4} + \sin^2 \frac{5 \pi}{4} + \sin^2 \frac{7 \pi}{4} =$$
$$\frac{\tan 40^\circ + \tan 20^\circ}{\cot 45^\circ - \cot 50^\circ \cot 70^\circ}$$
$$\tan A + \sin A = p; \tan A - \sin A = q \Rightarrow p^2 - q^2 = $$
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