Reasoning Coded Inequalities Questions and Study Materials
Directions(1-5): In the following questions, the symbols @, #, %, $ and * are used with the following meaning as illustrated below.‘A @ B’ means ‘A Is not smaller than B’
‘A # B’ means ‘A is neither smaller than nor equal to B’
‘A % B’ means ‘A is neither smaller than nor greater than B’
‘A $ B’ means ‘A is not greater than B’
‘A * B’ means ‘A is neither greater than nor equal to B’
1) Statements : T @ V, V # M, M % F
Conclusions : a) T # M
b) T @ F
2) Statements : L $ N, N * F, R % L
Conclusions : a) F # R
b) R $ N
3) Statements : H # I, I @ J, J $ P
Conclusions : a) H # J
b) H # P
4) Statements : L * D, D # K, K $ J
Conclusions : a) L * K
b) D $ J
5) Statements : Q $ W, W % E, E @ K
Conclusions : a) Q $ K
b) W @ K
Now in each of the following the questions assuming the given statements to be true, find which of the two conclusions a and b given below is/are definitely true?
Give answer a) : If only conclusion a is true
Give answer b) : If only conclusion b is true
Give answer c) : If either conclusion a or b is true
Give answer d) : If neither conclusion a nor b is true
Give answer e) : If both conclusions a and b are true ( Options are same for all questions (1-15) )
Explanation :
‘A @ B’ means ‘A Is not smaller than B’ → A ≥ B
‘A # B’ means ‘A is neither smaller than nor equal to B’ –> A > B
‘A % B’ means ‘A is neither smaller than nor greater than B’ –> A = B
‘A $ B’ means ‘A is not greater than B’ → A ≤ B
‘A * B’ means ‘A is neither greater than nor equal to B’ –> A < B
1) Answer : a) : If only conclusion a is true
Explanation : T @ V, V # M, M % F --> T ≥ V, V > M, M = F –> T ≥ V > M = F
Conclusion a –> T # M –> T > M
The relation between T and M in the statement T ≥ V > M = F : T > M. So, it is true.
Conclusion b –> T @ F –> T ≥ F
The relation between T and F in the statement T ≥ V > M = F : T > F. So, it is not true. ( T > M = F –> T > F )
2) Answer : e) : If both conclusions a and b are true
Explanation : L $ N, N * F, R % L → L ≤ N, N < F, R = L → R = L ≤ N < F
Conclusion a --> F # R –> F > R
The relation between F and R in the statement R = L ≤ N < F : R < F. So, it is true. ( R ≤ N < F --> R < F )
Conclusion b --> R $ N –> R ≤ N The relation between R and N in the statement R = L ≤ N < F : R ≤ N. So, it is true.
3) Answer : a) : If only conclusion a is true .
Explanation : H # I, I @ J, J $ P –> H > I, I ≥ J, J ≤ P –> H > I ≥ J ≤ P
Conclusion a –> H # J –> H > J
The relation between H and J in the statement H > I ≥ J ≤ P : H > J. So, it is true.
Conclusion b –> H # P –> H > P
The relation between H and P in the statement H > I ≥ J ≤ P : H > P or H < P or H = P. So, it is not true
4) Answer : d) : If neither conclusion a nor b is true .
Explanation : L * D, D # K, K $ J --> L < D, D > K, K ≤ J –> L < D > K ≤ J Conclusion a → L * K → L < K
The relation between L and K in the statement L < D > K ≤ J : L = K or L > K or L < K. So, it is not true.
Conclusion b --> D $ J –> D ≤ J
The relation between D and J in the statement L < D > K ≤ J : D = J or D > J or D < J. So, it is not true.
5) Answer : b) : If only conclusion b is true .
Explanation : Q $ W, W % E, E @ K --> Q ≤ W, W = E, E ≥ K –> Q ≤ W = E ≥ K Conclusion a –> Q $ K –> Q ≤ K
The relation between Q and K in the statement Q ≤ W = E ≥ K : Q = K or Q > K or Q < K. So, it is not true.
Conclusion b --> W @ K –> W ≥ K
The relation between W and K in the statement Q ≤ W = E ≥ K : W ≥ K. So, it is true.
Directions(6-10): 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’
‘P # Q’ means ‘P is not greater than Q’
‘P $ Q’ means ‘P is neither greater than nor equal to Q’
‘P © Q’ means ‘P is neither smaller than nor equal to Q’
‘P % Q’ means ‘P is neither greater than nor smaller than Q’
6) Statements : V $ W, W @ T, T # H
Conclusions : a) V © T
b) H % W
7) Statements : H © M, M @ E, E $ C
Conclusions : a) C © M b) H © E
8). Statements : N @ J, J % R, R © H
Conclusions : a) R # N
b) N © H
9) Statements : L @ K, K © A, A $ W
Conclusions : a) W $ L
b) L # W
10) Statements : J # R, R © D, D @ F
Conclusions : a) F $ R
b) F % R
Explanation :
‘P @ Q’ means ‘P is not smaller than Q’ → P ≥ Q
‘P # Q’ means ‘P is not greater than Q’ → P ≤ Q
‘P $ Q’ means ‘P is neither greater than nor equal to Q’ → P < Q
‘P © Q’ means ‘P is neither smaller than nor equal to Q’ → P > Q
‘P % Q’ means ‘P is neither greater than nor smaller than Q’ → P = Q
6) Answer : d) : If neither conclusion a nor b is true .
Explanation : V $ W, W @ T, T # H –> V < W, W ≥ T, T ≤ H --> V < W ≥ T ≤ H
Conclusion a --> V © T –> V > T
The relation between V and T in the statement V < W ≥ T ≤ H : V = T or V > T or V < T. So, it is not true.
Conclusion b --> H % W –> H = W The relation between H and W in the statement V < W ≥ T ≤ H --> H = W or H > W or H < W. So, it is not true.
7) Answer : b) : If only conclusion b is true .
Explanation : H © M, M @ E, E $ C –> H > M, M ≥ E, E < C → H > M ≥ E < C
Conclusion a --> C © M –> C > M
The relation between C and M in the statement H > M ≥ E < C --> M > C. So, it is not true.
Conclusion b –> H © E –> H > E The relation between H and E in the statement H > M ≥ E < C --> H > E. So, it is true.
8). Answer : e) : If both conclusions a and b are true .
Explanation : N @ J, J % R, R © H → N ≥ J, J = R, R > H → N ≥ J = R > H
Conclusion a –> R # N –> R ≤ N
The relation between R and N in the statement N ≥ J = R > H : N ≥ R. So, it is true.
Conclusion b –> N © H –> N > H
The relation between N and H in the statement N ≥ J = R > H : N > H. So, it is true.
9) Answer : d) : If neither conclusion a nor b is true .
Explanation : L @ K, K © A, A $ W → L ≥ K, K > A, A < W → L ≥ K > A < W
Conclusion a --> W $ L –> W < L
The relation between W and L in the statement L ≥ K > A < W : W = L or W > L or W < L . So, it is not true.
Conclusion b --> L # W –> L ≤ W
The relation between L and W in the statement L ≥ K > A < W : L = W or L < W or L > W. So, it is not true.
10) Answer : a) : If only conclusion a is true .
Explanation : J # R, R © D, D @ F → J ≤ R, R > D, D ≥ F → J ≤ R > D ≥ F
Conclusion a –> F $ R –> F < R
The relation between F and R in the statement J ≤ R > D ≥ F : R > F. So, it is true.
Conclusion b –> F % R –> F = R
The relation between F and R in the statement J ≤ R > D ≥ F : R > F. So, it is not true.
Directions(11-15): In the following questions, the symbols @, ©, %, $ and #
are used with the following meaning as illustrated below.
‘P % Q’ means ‘P is either smaller than or equal to Q’
‘P © Q’ means ‘P is grater than Q’
‘P # Q’ means ‘P is neither greater than nor smaller than Q’
‘P $ Q’ means ‘P is smaller than Q’
‘P @ Q’ means ‘P is either greater than or equal to Q’
11) Statements : B # F, F $ H, H © K
Conclusions :a) H @ B
b) K $ B
12) Statements : H @ T, T © N, N $ W
Conclusions : a) N $ H
b) W $ H
13) Statements : H $ F, F % M, M © J
Conclusions : a) J $ F
b) M © H
14) Statements : M $ T, T % R, M © N
Conclusions : a) M $ R
b) N $ T
15) Statements : D $ T, T % B, B @ F
Conclusions : a) D # T
b) D @ F
Explanation :
‘P % Q’ means ‘P is either smaller than or equal to Q’ –> P ≤ Q
‘P © Q’ means ‘P is greater than Q’ –> P > Q
‘P # Q’ means ‘P is neither greater than nor smaller than Q’ –> P = Q
‘P $ Q’ means ‘P is smaller than Q’ → P < Q
‘P @ Q’ means ‘P is either greater than or equal to Q’ --> P ≥ Q
11) Answer : d) : If neither conclusion a nor b is true .
Explanation : B # F, F $ H, H © K → B = F, F < H, H > K → B = F < H > K
Conclusion a –> H @ B –> H ≥ B
The relation between H and B in the statement B = F < H > K : B < H. So, it is not true.
Conclusion b --> K $ B –> K < B
The relation between K and B in the statement B = F < H > K : K = B or K > B or K < B. So, it is not true.
12) Answer : a) : If only conclusion a is true.
Explanation : H @ T, T © N, N $ W → H ≥ T, T > N, N < W → H ≥ T > N < W
Conclusion a –> N $ H –> N < H
The relation between N and H in the statement H ≥ T > N < W : H > N. So, it is true.
Conclusion b –> W $ H –> W < H
The relation between W and H in the statement H ≥ T > N < W : W = H or W > H or W < H. So, it is not true.
13) Answer : b) : If only conclusion b is true .
Explanation : H $ F, F % M, M © J → H < F, F ≤ M, M > J → H < F ≤ M > J
Conclusion a –> J $ F –>J < F
The relation between J and F in the statement H < F ≤ M > J : J = F or J < F or J > F. So, it is not true.
Conclusion b –> M © H –> M > H
The relation between M and H in the statement H < F ≤ M > J : M > H. So, it is true.
14) Answer : e) : If both conclusions a and b are true .
Explanation : M $ T, T % R, M © N → M < T, T ≤ R, M > N → N < M < T ≤ R
Conclusion a --> M $ R –> M < R
The relation between M and R in the statement N < M < T ≤ R : M < R. So, it is true.
Conclusion b --> N $ T –> N < T
The relation between N and T in the statement N < M < T ≤ R : N < T. So, it is true.
15) Answer : d) : If neither conclusion a nor b is true .
Explanation : D $ T, T % B, B @ F → D < T, T ≤ B, B ≥ F → D < T ≤ B ≥ F Conclusion a --> D # T –> D = T
The relation between D and T in the statement D < T ≤ B ≥ F : D < T. So, it is not true. Conclusion b → D @ F → D ≥ F
The relation between D and F in the statement D < T ≤ B ≥ F : D < F. So, it is not true
