Relations Test 39

Result

Relations Test 39

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Weekly Quiz Competition

Question 1
1 / -0

$$p \Rightarrow \,q$$ can also be written as

A
$$p \Rightarrow \, \sim q$$

B
$$ \sim p \vee q$$

C
$$ \sim q \Rightarrow \, \sim p$$

D
None of these

Solution
Question 2
1 / -0

If $$R$$ is relation is "greater then or equal" from $$A=\left\{1,2,3,4\right\}$$ to $$B=\left\{4,5,6\right\}$$, then $$R^{-1}=$$

A
$$\left\{(4,4)\right\}$$

B
$$\phi$$

C
$$A\ x\ B$$

D
$$R$$

Solution

Question 3

1 / -0

Which of the following is always true

$$(p\Longrightarrow q)\equiv \sim q\Longrightarrow \sim p$$

$$\sim (p\Longrightarrow q)\equiv p\ \wedge \sim q$$

$$\sim (p\ \vee q)\equiv \vee\ p\ \vee \sim q$$

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

Solution

Truth table:

$$p$$	$$q$$	$$p\Rightarrow q$$	$$\sim q$$	$$\sim p$$	$$\sim q\Rightarrow \sim p$$
$$T$$	$$T$$	$$T$$	$$F$$	$$F$$	$$T$$
$$T$$	$$F$$	$$F$$	$$T$$	$$F$$	$$F$$
$$F$$	$$T$$	$$T$$	$$F$$	$$T$$	$$T$$
$$F$$	$$F$$	$$T$$	$$T$$	$$T$$	$$T$$

So, $$(p\Rightarrow q)\cong \sim q\Rightarrow \sim p$$

Question 4
1 / -0

If $$A={a,b,c,d,e}$$, then the number of equivalence relations on $$A$$ is

A
$$26$$

B
$$52$$

C
$$54$$

D
$$63$$

Solution
Question 5
1 / -0

The relation $$R=\left\{(1, 1), (2, 2), (3, 3)\right\}$$ on the set $$\left\{1, 2, 3\right\}$$ is

A
symmetric only

B
reflexive only

C
an equivalence relation

D
transistive only

Solution
Question 6
1 / -0

The number of ordered pairs (x, y) of natural numbers satisfy the equation $$x^2+y^2+2xy-2018x-2018y-2019^o=0$$ is?

A
$$0$$

B
$$1009$$

C
$$2018$$

D
$$2019$$

Solution
Question 7
1 / -0

Let xyz =105 where x,y,z,then number of ordered triplets (x,y,z) satisfying the given equation

A
15

B
27

C
6

D
33

Solution
Question 8
1 / -0

Let $$N$$ be the set of all positive integers and $$\phi$$ be a relation on $$N\times \ N$$ defined by $$(a,b)\times (c,d)$$. If $$ad(b+c)=bc(a+d)$$ then $$\phi$$ is

A
symmetric only

B
reflexive only

C
transitive only

D
an equivalence relation

Solution
Question 9
1 / -0

Let $$f:R\rightarrow R$$ be defined as
$$f(x)={ x }^{ 3 }+{ 2x }^{ 2 }+4x+sin\left( \dfrac { \pi x }{ 2 } \right) $$ and $$g(x)$$be the inverse function of f(x), then $${ g }^{ ' }(8)$$is equal to :

A
$$\dfrac { 1 }{ 2 } $$

B
9

C
$$\dfrac { 1 }{ 11 } $$

D
11

Solution
Question 10
1 / -0

Let $$X$$ be a family of sets and $$R$$ be a relation on $$X$$ defined by $$'A$$ is disjoint from $$B ^ { \prime }$$ . Then $$R$$ is _________.

A
Reflexive

B
Symmetric

C
Anti-symmetric

D
Transitive

Solution