p : Musa is short
q : Musa is brilliant
Which of the following represents the statement "Musa is short but not brilliant"?
p∨q
p∨∼q
p∧∼q
p∧q
Correct answer is C
No explanation has been provided for this answer.
−12
0
23
2
Correct answer is A
Given the formula for p * q as: p+q+2pq and its identity element is 0, such that if, say, t is the inverse of p, then
p∗t=0, then p+t+2pt=0∴
t = \frac{-1}{1 + 2p} is the formula for the inverse of p and is undefined on R when
1 + 2p) = 0 i.e when 2p = -1; p = \frac{-1}{2}.
Express \frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}} in the form p\sqrt{3} + q\sqrt{2}
7\sqrt{3} - \frac{17\sqrt{2}}{3}
7\sqrt{2} - \frac{17\sqrt{3}}{3}
-7\sqrt{2} + \frac{17\sqrt{3}}{3}
-7\sqrt{3} - \frac{17\sqrt{2}}{3}
Correct answer is B
Given \frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}},
first, we rationalise by multiplying through with 2\sqrt{3} - 3\sqrt{2} (the inverse of the denominator).
(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}})(\frac{2\sqrt{3} - 3\sqrt{2}}{2\sqrt{3} - 3\sqrt{2}})
= \frac{16\sqrt{3} - 24\sqrt{2} - 18\sqrt{2} + 18\sqrt{3}}{4(3) - 6\sqrt{6} + 6\sqrt{6} - 9(2)}
= \frac{34\sqrt{3} - 42\sqrt{2}}{-6} = 7\sqrt{2} - \frac{17\sqrt{3}}{3}
{x : -5 < x < 5}
{x : -5 \leq x \leq 5}
{x : -5 \leq x < 5}
{x : -5 < x \leq 5}
Correct answer is A
P = {x : -2 < x < 5} and Q = {x: -5 < x < 2}
(P \cup Q) = {x : -5 < x < 5}
x^{2} + 4x - 5
x^{2} - 4x + 5
x^{2} - 1
x - 1
Correct answer is B
f(x) = x^{2} + 1 and g(x) = x - 2
f o g = f(g(x)) = f(x - 2) = (x - 2)^{2} + 1
= x^{2} - 4x + 4 + 1 = x^{2} - 4x + 5