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# Inequality - Solved Examples

In the following question, some symbols are used with the letters having the following meanings as illustrated below −

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Now, in each of the following questions, assuming the given statements to be valid, find out which of the two conclusions I and II given below them is /are definitely valid.

Q 1 − Statements: P@Q, Q!R, R$S

Conclusions:

I. S#P

II. S#Q

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - D**

**Explanation**

Neither S is higher than or equal to P nor S is higher than or equal to Q. Hence option D is correct.

In the following question, some symbols are used with the letters having the following meanings as illustrated below −

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Now, in each of the following questions, assuming the given statements to be valid, find out which of the two conclusions I and II given below them is /are definitely valid.

Q 2 − Statements: A@B, B!C, C$D

Conclusions:

I. D@B

II. D∗A

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - A**

**Explanation**

Here only D is higher than B. Hence option A is correct.

In the following question, some symbols are used with the letters having the following meanings as illustrated below −

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Now, in each of the following questions, assuming the given statements to be valid, find out which of the two conclusions I and II given below them is /are definitely valid.

Q 3 − Statements: P#S, S@R, P∗N

Conclusions:

I. N$R

II. P@R

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - B**

**Explanation**

Here only P is higher than R. Hence option b is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 4 − Statements: N$S, S@R, R#Q, Q#T

Conclusions:

I. N@R

II. R#T

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - E**

**Explanation**

Both the conclusions are valid, hence option E is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 5 − Statements: P!S, S#N, N@R, P!Q

Conclusions:

I. Q@S

II. S@R

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - B**

**Explanation**

Only S is higher than R is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 6 − Statements: C$D, D@E, D!G, C#P, P@N

Conclusions:

I. D#P

II. C!G

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - E**

**Explanation**

Both the conclusions are valid. Hence option E is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 7 − Statements: Z$R, R∗Q, Q#P, P!K

Conclusions:

I. Z#Q

II. P!Z

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - D**

**Explanation**

Neither I nor II is valid. Hence option D is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 8 − Statements: P#S, S@R, P∗N

Conclusions:

I. N$S

II. N@S

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - C**

**Explanation**

Here either N is higher than or equal to S. Hence option C is chosen.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 9 − Statements: M#Q, Q$Z, M∗N

Conclusions:

I. N$Z

II. M@Z

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - B**

**Explanation**

Here only M is higher than Z. Hence option B is correct.

R∗S suggests that R is not higher than S

R@S suggests that R is neither shorter than nor equal to S

R!S suggests that R is neither higher than nor equal to S

R$S suggests that R is neither shorter nor higher than S

R#S suggests that R is not shorter than S

Q 10 − Statements: A#B, B@C, A∗D

Conclusions:

I. D$B

II. D@B

Give answer −

A - If only conclusion I is valid.

B - If only conclusion II is valid.

C - If either conclusion I or II is valid.

**Answer - C**

**Explanation**

Here either D is higher than B or equal to B. Hence option C is chosen.