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Recent questions and answers in Discrete Mathematics
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TN XII Math
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Discrete Mathematics
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
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q22
answered
May 24
by
benitaoliva23
1
answer
Show that the set $ G = \{2^n / n \in Z\} $ is an abelian group under multiplication.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q12
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.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q11
modelpaper
mar-2008
answered
Sep 16, 2013
by
sreemathi.v
1
answer
Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q10
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.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q9
modelpaper
mar-2007
jun-2009
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 $a, b \in G$.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q8
modelpaper
jun-2007
mar-2009
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.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q7
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.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q6
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 $a, b \in G.$
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q5
modelpaper
mar-2006
jun-2006
oct-2007
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
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q4
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?
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q3
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?
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q2
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.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q1
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that $(p \wedge q)\rightarrow (p \vee q)$ is a tautology.
bookproblem
ch9
sec1
exercise9-3
p168
q7
tnstate
class12
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that $p \rightarrow q$ and $q \rightarrow p$ are not equivalent.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q6
modelpaper
mar-2009
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that $\sim(p\wedge q) \equiv (\sim p)\vee (\sim q)$
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q5
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that p ↔ q ≡ ((∼ p) ∨ q) ∧ ((∼ q) ∨ p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q4
modelpaper
mar-2007
jun-2007
oct-2008
mar-2010
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that p ↔ q ≡ (p → q) ∧ (q → p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q3
modelpaper
oct-2006
jun-2009
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Show that p → q ≡ (∼ p) ∨ q
tnstate
class12
bookproblem
ch9
sec2
exercise9-3
p168
q2
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-5
modelpaper
jun-2008
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-4
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-3
modelpaper
oct-2009
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-2
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-1
answered
Sep 13, 2013
by
sreemathi.v
1
answer
Construct the truth tables for the following statement: (p ∧ q) ∨ r
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q10
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (p ∨ q) ∨ r
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q9
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q8
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ [∼ (p ∧ q)]
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q7
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: ∼ (p ∨ (∼ q))
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q6
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q5
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (p ∨ q) ∨ (∼ p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q4
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: ∼ (p ∨ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q3
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement: (∼ p) ∧ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q2
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Construct the truth tables for the following statement :p ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q1
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Write negation of the each of the following statements :
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q25
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
If p stands for the statement “Sita likes reading” and q for the statement “Sita likes playing’ what does ∼p ∧ ∼ q stand for?
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q24
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Translate each of the following compound statements into symbolic form:
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q23
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.
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q21
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
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p160
q1-10
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
Write down the truth value (T or F) of the following statements
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p160
q11-20
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
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