# Mathematical Operations / Inequalities – Set 21

D.1-5) In the following Questions @, #, %, * and \$ are used according to following Meanings :

‘A @ B’ means, ‘A is not smaller than B’

‘A # B’ means, ‘A is not greater than B’

‘A % B’ means, ‘A is neither greater nor equal to B’

‘A * B’ means, ‘A is neither smaller nor greater than B’

‘A \$ B’ means, ‘A is neither smaller nor equal to B’

Now from the following statements, check whether the following conclusions I,II and III are definitely true.

1) Statements:

B#N, C@N, T\$C

Conclusions:

I.B%T

II. T\$N

III. N@B

(a) None is true

(b) I and II are true

(c) II and III are true

(d) All are true

(e) I and III are true

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(d)

A@B -> A≤B

A#B -> A≤B

A%B-> A<B

A*B -> A=B

A\$B ->A>B

B≤N≤C<T

1. B<T True
2. T>N True
3. N≥B True

2) Statements:

J@M, A\$M, T#J

Conclusions:

I. T#A

II. J@A

III. T\$M

(a) Only I is true

(b) Only II is true

(c) Only III is true

(d) None is true

(e) All are true

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(d)

A@B -> A≤B

A#B -> A≤B

A%B-> A<B

A*B -> A=B

A\$B ->A>B

T≤J≥M<A

1. T≤A False
2. J≥A False
3. T>M False

3) Statements:

F\$K, K#D, D*H

Conclusions:

I. H*k

II. H%F

III. H \$ k

(a) All are true

(b) Either I or II are true

(c) Either I or III are true

(d) Either II or III are true

(e) None of these

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(c)

A@B -> A≤B

A#B -> A≤B

A%B-> A<B

A*B -> A=B

A\$B ->A>B

F>K≤D=H

1. H=K False
2. H<F False
3. H>K False

4) Statements:

X*D, D@Y, Y%Z

Conclusions:

I.X*Z

II.X \$ Z

III. D \$ Z

(a) Only I is true

(b) None is true

(c) Only III is true

(d) Only II is true

(e) All are true

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(b)

A@B -> A≤B

A#B -> A≤B

A%B-> A<B

A*B -> A=B

A\$B ->A>B

X=D≥Y<Z

1. X=Z False
2. X>Z False
3. D>Z False

5) Statements:

U%R, R#V, V*M

Conclusions:

I.M*R

II.M\$R

III. M\$U

(a) All are true

(b) Either I or II are true

(c) Either I or II and III are true

(d) Either I or III and II are true

(e) None of these

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(c)

A@B -> A≤B

A#B -> A≤B

A%B-> A<B

A*B -> A=B

A\$B ->A>B

U<R≤V=M

1. M=R False
2. M>R False
3. M>U True

D.6-10) : Study the following information to answer the given Questions :

J\$R means J is not smaller than R

J@R means J is neither smaller than nor equal to R

J#R means J is neither greater than nor equal to R

J&R means J is neither greater than nor smaller than R

J*R means J is not greater than R

6) Statements: W \$ N, P@ H, K # P, W\$H

Conclusions:

I.K # H

II. W @ P

III. H * W

IV. N # P

(a) Only I is true

(b) None is true

(c) Only III is true

(d) Only II is true

(e) Only IV is true

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(c)

J\$R -> J≥R

J@R -> J>R

J#R -> J<R

J&R -> J=R

J*R -> J≤R

K<P>H≤W≥N

1. K<H False
2. W>P False
3. H≤W True
4. N<P False

7) Statements:

W * G, K * F, G @ X, W @ K

Conclusions:

I. G @ K

II. W \$ G

III. W @ G

IV. W @ X

(a) Only II is true

(b) None is true

(c) Only III and IV are true

(d) Only I is true

(e) Only I and IV are true

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(d)

J\$R -> J≥R

J@R -> J>R

J#R -> J<R

J&R -> J=R

J*R -> J≤R

F ≥K<W≤G>X

1. G>K True
2. W≥G False
3. W>G False
4. W>X False

8) Statements:

R * Y, S # N, Y \$ S, N @ J

Conclusions:

I. J # S

II. Y @ N

III. R # N

IV. Y @ J

(a) Only II is true

(b) None is true

(c) Only III is true

(d) Only I is true

(e) Only IV is true

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(b)

J\$R -> J≥R

J@R -> J>R

J#R -> J<R

J&R -> J=R

J*R -> J≤R

R≤Y≥S<M>J

1. J<S False
2. Y>N False
3. R<N False
4. Y>J False

9) Statements:

A @ K, K # N, N & B, B * W

Conclusions:

1. W \$ N
2. B @ K
3. A @ W
4. K @ W

(a) I, II, and III are true

(b) I, II are true

(c) I, III are true

(d) I,III and IV are true

(e) All are true

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(b)

J\$R -> J≥R

J@R -> J>R

J#R -> J<R

J&R -> J=R

J*R -> J≤R

A>K<N=B≤W

1. W≥N True
2. B>K True
3. A>W False
4. K>W False

10) Statements:

D # O, O * K, K @ R, R \$ N

Conclusions:

I. N # O

II. N @ K

III. O # R

IV. K # D

(a) Only II is true

(b) None of these

(c) Only III is true

(d) Only I is true

(e) None is true

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(e)

J\$R -> J≥R

J@R -> J>R

J#R -> J<R

J&R -> J=R

J*R -> J≤R

D<O≤K>R ≥N

1. N<O False
2. N>K False
3. O<R False
4. K<D False