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Published on: 02/09/2022
QB365 provides a detailed and simple solution for every Possible Creative Questions in Class 12 Maths Subject - Discrete Mathematics, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
Download Tamil Nadu 12th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
The probability distribution of a random variable is given below
| X = x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X = x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2+k |
2.
Construct the truth table for (-p) v (q ∧ r)
3.
In (z, *) where * is defined as a * b = a + b + 2. Verify the commutative and associative axiom.
4.
Let G = {1, i, -1, -i} under the binary operation multiplication. Find the inverse of all the elements.
5.
In (z, *) where * is defined by a * b = ab, prove that * is not a binary operation on z.
6.
Write the truth value for each of the following statements.
(1) 3 + 5 = 8 and \(\sqrt{2}\) is an irrational number.
(2) 5 is a positive integer or a square is a rectangle.
(3) Chennai is not in Tamilnadu.
7.
Show that ¬( p ∧ q) ≡ ¬p V ¬q
1.
| X = x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X = x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2+k |
\(\sum f(x) 0=1\)
\( 0+k+2 k+2 k+3 k+k^{2}+2 k^{2}+7 k^{2}+k =1 \)
\(10 k^{2}+9 k-1=0 \)
\( (10 k-1)(k+1)=0 \)
P (0<x<4) = P(X = 1) + P(X = 2) + P(X = 3)
\( =\mathrm{k}+2 \mathrm{k}+2 \mathrm{k} \)
\(=5 \mathrm{k} \)
\( =\frac{5}{10}=\frac{1}{2} \)
2.
| p | q | r | ~p | q ∧ r | (~p) v (q ∧ r) |
| T | T | T | F | T | T |
| T | F | F | F | F | F |
| T | F | T | F | F | F |
| T | F | F | F | F | F |
| F | T | T | T | T | T |
| F | T | F | T | F | T |
| F | F | T | T | F | T |
| F | F | F | T | F | T |
3.
(a) Let a, b \(\in \) 2.
The a * b = a + b + z = b + a + z = b * a
(z, *) has commutative property.
(b) Let a, b, c \(\in \) G
(a * b) * c = (a+b+2) * c = a + b + 2 + c + 2
= a + b + c + 4
∴ z is associate under *.
4.
Clearly 1 is the identity element of (G1)
Inverse of 1 is 1 [∴ (1)(1) = 1]
Inverse of i is -i [∴ (i) (-i) = -i2 = 1]
Inverse of -1 is -1 [∴ (-1)(-1) = 1]
Inverse of is i [∴ (-i)(i) = -i2 = 1]
5.
Let a = 2, b = -5
∴ a * b = ab
⇒ 2 * -5 = 2-5 = \(\frac{1}{2^5}\) ∉ z
* is not a binary operation on z.
6.
(1) p: 3+5 = 8
q: . \(\sqrt{2}\) is an irrational number.
T and T = T
(2) p: 5 is a positive integer.
q: A square is a rectangle.
T or F = T
(3) p: Chennai is not in Tamilnadu F.
7.
~( p ∧ q) ≡ ~p V ~q
| p | q | p ∧ q | ~(p ∧ q) | ~p | ~p | ~p V ~q |
| T | T | T | F | F | F | F |
| T | F | F | T | F | T | T |
| F | T | F | T | T | F | T |
| F | F | F | T | T | T | T |
From column (4) and column (7), the entries are Identical.
ஃ ~( p ∧ q) ≡ ~p V ~q are identical and hence they are equivalent.
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