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Solved Example

Read the following instructions:
[email protected] means “A is greater than B”
A#B means “A is smaller than B”
A$B means “A is equal to B”

Statements:
I. [email protected], [email protected]
II. M$N, N$P


Conclusions:
A. Z#X ---------- True (Z is smaller than X)
B. P$M---------- True ( P=M)
C. X$Z------------ False (X is not equal to Z)

 

Illustration 2

In the following questions, the symbols $, @, ©, % and * are used with the following meaning as illustrated below:

 

P$Q’ means ‘P is not smaller than Q’

 

[email protected]’ means ‘P is not greater than Q’

 

P©Q’ means that ‘P is neither greater than nor smaller than Q’

 

P%Q’ means ‘P is neither smaller than nor equal to Q’

 

P*Q’ means ‘P is neither greater than nor equal to Q’

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true?Give answer (a) if only conclusions I is true.

Give answer (b) if only conclusion II is true. Give answer (c) if either conclusion I or II is true. Give answer (d) if neither conclusion I nor, II is true. Give answer (e) if both the conclusion I and II are true.
 

 
Example-1

Statements: K @ B, B * J, J © T

Conclusions: I. K*T II. [email protected]
 

 
Example-2

Statements: F $ M, M @ L, L*W

Conclusions: I. W$M II. [email protected]
 

 
Example-3

Statements: R * Q, Q @ F, F % A

Conclusions: I. R©A II. R*F
 

 
Example-4

Statements: V $ X, X © Y, Y % H

Conclusions: I. [email protected] II. H*V
 

 
Example-5

Statements: M @ B, B * A, A @ F

Conclusions: I. M*A II. B*F
 

 
Solutions

(1 to 5): P$Q------P ≥ Q [email protected] ---- P ≤ Q P©Q ------P = Q P%Q ------P > Q P*Q ------ P < Q

  1. (a) : K @ B – K ≤ B…..(I)
     
    B * J - B < J….(II)
     
    J © T - J = T….(III)
     
    Hence, K ≤ B < J = T
     
    Conclusions: I. K * T ---- K < T------ Form (I), (II), (III), true
     
    II. B @ T --------- B ≤ T ----- Form (II) not true.
     
    So, answer is (a).
  2. (d) : F $ M ---------- F ≥ M
     
    M @ L -------- M ≤ L
     
    L * W ---------- L < W
     
    Hence, F ≥ M ≤ L < W
     
    Conclusions: I. W $ M -------- W ≥ M
     
    II. F @ L ------- F ≤ I;
     
    So, answer is (d).
  3. (b) : R * Q ------ R < Q
     
    Q @ F ------ Q ≤ F
     
    F % A ----- F > A
     
    Hence, R < Q ≤ F > A
     
    Conclusions: I. R © A ----- R = A
     
    II. R * F ----- R < F;
     
    So, answer is (b).
  4. (e) : V $ X ----- V ≥ X
     
    X © Y ------ X = Y
     
    Y % H ----- Y > H
     
    Hence, V ≥ X = Y > H
     
    Conclusions: I. Y @ V ------ Y ≤ V
     
    II. H * V ------ H < V;
     
    So, answer is (e).
  5. (e): M @ B ---- M ≤ B
     
    B * A ----- B < A
     
    A @ F ------ A ≤ F
     
    Hence, M ≤ B < A ≤ F
     
    Conclusions: I. M * A ----- M < A
     
    II. B * F ----- B < F;
     
    So, answer is (e).




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