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Recent questions and answers in Discrete Mathematics

Questions >> TN XII Math >> Discrete Mathematics

If p stands for the statement “Sita likes reading” and q for the statement “Sita likes playing’ what does ∼p ∧ ∼ q stand for?

answered Jan 24, 2022 by manojvikvetrivel2004

1 answer

Write down the truth value (T or F) of the following statements

answered Aug 16, 2021 by randyranjith214

1 answer

Let p be “Kamala is going to school” and q be “There are twenty students in the class “. Give a simple verbal sentence which describes each of the following statements : (i) p ∨ q (ii) p ∧ q (iii) ∼ p (iv) ∼ q (v) ∼p ∨ q

answered May 24, 2021 by benitaoliva23

1 answer

Show that the set $ G = \{2^n / n \in Z\} $ is an abelian group under multiplication.

answered Sep 16, 2013 by sreemathi.v

1 answer

Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.

answered Sep 16, 2013 by sreemathi.v

1 answer

Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$

answered Sep 16, 2013 by sreemathi.v

1 answer

Show that the set {[1], [3], [4], [5], [9]} forms an abelian group under multiplication modulo 11.

answered Sep 16, 2013 by sreemathi.v

1 answer

Show that the set G of all rational numbers except − 1 forms an abelian group with respect to the operation $$ given by $a b = a + b + ab$ for all $a, b \in G$.

answered Sep 16, 2013 by sreemathi.v

1 answer

Show that the set M of complex numbers z with the condition | z | = 1 forms a group with respect to the operation of multiplication of complex numbers.

answered Sep 14, 2013 by sreemathi.v

1 answer

Show that { $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega & 0 \\ 0 & \omega^2\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega^2 & 0 \\ 0 & \omega\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega^2\\ \omega & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega\\ \omega^2 & 0\end{smallmatrix} \bigr) $} where $\omega^3 = 1, \omega \neq 1$ form a group with respect to matrix multiplication.

answered Sep 14, 2013 by sreemathi.v

1 answer

Show that the set G of all positive rationals forms a group under the composition $$ defined by $a b = (\large\frac{ab}{3})$ for all $a, b \in G.$

answered Sep 14, 2013 by sreemathi.v

1 answer

Prove that the matrices $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr) $ form a group under matrix multiplication

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that the set N of natural members is a semi-group under the operation $x * y $= max {x, y}. Is it a monoid?

answered Sep 13, 2013 by sreemathi.v

1 answer

Let $S$ be a non-empty set and o be a binary operation on $S$ defined by $xoy = x ; x, y \in S$. Determine whether o is commutative and associative.

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that $(p \wedge q)\rightarrow (p \vee q)$ is a tautology.

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that $p \rightarrow q$ and $q \rightarrow p$ are not equivalent.

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that $\sim(p\wedge q) \equiv (\sim p)\vee (\sim q)$

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that p ↔ q ≡ ((∼ p) ∨ q) ∧ ((∼ q) ∨ p)

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that p ↔ q ≡ (p → q) ∧ (q → p)

answered Sep 13, 2013 by sreemathi.v

1 answer

Show that p → q ≡ (∼ p) ∨ q

answered Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

answered Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

answered Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

answered Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

answered Sep 13, 2013 by sreemathi.v

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

answered Sep 13, 2013 by sreemathi.v

1 answer

Construct the truth tables for the following statement: (p ∧ q) ∨ r

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (p ∨ q) ∨ r

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (p ∧ q) ∨ [∼ (p ∧ q)]

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: ∼ (p ∨ (∼ q))

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (p ∨ q) ∨ (∼ p)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: ∼ (p ∨ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement: (∼ p) ∧ (∼ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Construct the truth tables for the following statement :p ∨ (∼ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Write negation of the each of the following statements :

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Translate each of the following compound statements into symbolic form:

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Form the conjunction and the disjunction of (i) p : Anand reads newspaper, q : Anand plays cricket. (ii) p : I like tea. q : I like ice-cream.

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Find out which of the following sentences are statements and which are not? Justify your answer

asked Nov 27, 2012 by balaji.thirumalai

0 answers

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