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Recent questions tagged p4

What are the differences between a particle and a wave ?

asked May 18, 2017 by pady_1

1 answer

On the set N of natural numbers, define the operation * on N by mn=gcd(m,n) for all m, n$ \varepsilon$ N. Show that is commutative as well as associative.

asked Jan 23, 2013 by meena.p

0 answers

Determine which of the following functions \[f:R \rightarrow R\;are\;(a)One-One\quad(b)Onto\]\[(i)f(x)=|x|+x\]\[(ii)f(x)=x-[x]\]

asked Jan 23, 2013 by meena.p

0 answers

Let X = {1,2,3,4,5,6,7,8,9}. Let $ R_1\;andR_2$ be relations in x given by \[R_1=\{(x,y):x-y\;is\;divisible\;by\;3\}\;and\]\[R_2=\{(x,y)!\{x,y\} \varepsilon \{1,4,7\}or\{x,y\} \varepsilon \{2,5,8\}\]\[or \{x,y\} \varepsilon \{3,6,9\}\}.\; Show\; that \;R_1=R_2.\]

asked Jan 23, 2013 by meena.p

0 answers

Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.

asked Jan 23, 2013 by meena.p

1 answer

Show that the function $ f:N \rightarrow N$ given by $f(x) = x -(-1)^x\;for\;all\;x\; \varepsilon\;N $ is a bijection.

asked Jan 23, 2013 by meena.p

0 answers

Define a binary operation $^$ on the set A = {0,1,2,3,4,5} as \[ab=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\]Show that zero is an identity element for this operation and each element a of the set is invertiable with 6-a being the inverse of a.

asked Jan 23, 2013 by meena.p

0 answers

Let f and g be real valued functions, such that $(fog)(x)=\cos x^3\; and\;(gof)(x)=\cos^3x,$ find the functions f and g.

asked Jan 23, 2013 by meena.p

0 answers

Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.

asked Jan 23, 2013 by meena.p

1 answer

Prove that the inverse of an equivalence relation is an equivalence relation.

asked Jan 23, 2013 by meena.p

0 answers

Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.

asked Jan 23, 2013 by meena.p

1 answer

Let a relation R on the set R of real numbers defined as $(x,y)\; \varepsilon\;R \Leftrightarrow x^24xy+3y^2\;=\;0.$Show that R is reflexive but neither symmetric nor transitive.

asked Jan 23, 2013 by meena.p

0 answers

Let a relation R on the set R of real numbers be defined as $ (a,b) \varepsilon R \Leftrightarrow 1+ ab > 0 for\; all\; a, b\; \varepsilon\; R.$show that R is reflexive and symmetric but not transitive.

asked Jan 23, 2013 by meena.p

0 answers

If the function $ f\;:\;R \rightarrow A $ given by $f(x)=\frac{x^2}{x^2+1}$is surjection, find the set A.

asked Jan 23, 2013 by meena.p

0 answers

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