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Coded Inequalities

Here all the inequalities symbol coded in a symbol. At first, you need to decode the symbol then make a relation.

P $ Q means P is greater or equal to Q

P @ Q means P is less than or equal to Q

P % Q means P is greater than Q

P © Q means P is less than Q

P * Q means P is equal to Q

Statement:

Ex. 1: A $ B, B % C, C * D

Conclusion

(I) A % D

(II) B $ D

Solution:

A $ B means A ≥ B

B % C means B ≥ C

C * D means C = D

A ≥ B ≥ C = D

Now A % D means A > D which is not true

B $ D means B ≥ D which we can conclude from the decoded inequalities

So, the answer will be only (II) follows.

So, option (b) is correct.

Example – 1

M @ N @ O, O * P © Q, Q % R @ T $ S

Conclusion:

(I) M © Q

(II) O * S

(a) Only (I) follow

(b) Only (I) and (II) follow

(c) Only (II) and (III) follow

(d) All follow

(e) None follows

Solution:

After decoding

M @ N @ O means  M ≤ N ≤ O

O * P © Q means O = P < Q

Q % R @ T $ S means Q > R ≤ T  ≥ S

Combining these we can get.

M ≤ N ≤ O = P < Q > R ≤ T ≥ S

Now, M © Q means M < Q

M ≤ N ≤ O = P < Q which implies M < Q

Now O * S means O = S which is not true

Now N @ R means N ≤ R. There is a direction change in the symbol so it is not true

So, only conclusion (I) follows.

So, option (a) is correct.

Example – 2

Statement

E $ F * G $ H, H % I % J $ K, K @ L * M

Conclusion

(I) E % I

(II) K © F

(III) E * M

(a) Only (I) follow

(b) Only (I) and (II) follow

(c) All follow

(d) Only (II) and (III) follow

(e) None follows

Solution:

After decoding

E $ F * G $ H means E ≥ F = G ≥ H

H % I % J $ K means H > I > J ≥ K

K @ L * M means K ≤ L = M

After combining this.

E ≥ F = G ≥ H > I > J ≥ K ≤ L = M

E % I means E > I

E ≥ F = G ≥ H > I which implies E > I

K © F means K < F

E ≥ F = G ≥ H > I > J ≥ K, which implies F > K 

Means K < F

E * M means E = M which is not true

So, only (I) and (II) follow.

So, option (b) is correct.