Mathematical operation and symbol notation Difficult Questions and Answers

Mathematical operation and symbol notation

Direction: In the following questions, the symbols δ, $, ∗ , @ and © are used with the meaning as indicated below.
'P $ Q' means 'P is neither equal to nor greater than Q'.
'P © Q' means 'P is neither equal to nor smaller than Q'
'P δ Q' means 'P is neither greater than nor smaller to Q'.
'P @ Q' means 'P is not smaller than Q'.
'P ∗ Q' means 'P is not greater than Q'.
in each question, three statements showing relationship, have been given , which are followed by three Conclusions I, II and III. Assuming that the given statements to be true, find out which conclusion(s) is/are definitely true.

Statements
F ∗ T, T $ N, N @ R
Conclusions
I. R $ T
II. N © F
III. F $ R

Statements
F ∗ T ⇒ F ≤ T,
T $ N ⇒ T < N, N @ R ⇒ N ≥ R
So, F ≤ T < N ≥ R
Conclusions
I. R $ T ⇒ R < T      (false)
II. N © F ⇒ N > F      (true)
III. F $ R ⇒ F < R      (false)

Correct Option: C

Statements
F ∗ T ⇒ F ≤ T,
T $ N ⇒ T < N, N @ R ⇒ N ≥ R
So, F ≤ T < N ≥ R
Conclusions
I. R $ T ⇒ R < T      (false)
II. N © F ⇒ N > F      (true)
III. F $ R ⇒ F < R      (false)
So, only Conclusion II is true from the given statements.

Statements
M @ D, D δ K, K © R
Conclusions
I. R $ M
II. K δ M
III. K $ M

Statements
M @ D ⇒ M ≥ K,
D δ K ⇒ D = K, K © R ⇒ K > R
So, M ≥ K = D > R
Conclusions
I. R $ M ⇒ R < M      (true)
II. K δ M ⇒ K = M      ( may be)
III. K $ M ⇒ K < M      ( may be)

Correct Option: D

Statements
M @ D ⇒ M ≥ K,
D δ K ⇒ D = K, K © R ⇒ K > R
So, M ≥ K = D > R
Conclusions
I. R $ M ⇒ R < M      (true)
II. K δ M ⇒ K = M      ( may be)
III. K $ M ⇒ K < M      ( may be)
So, from the given statements either II or III and I are true.

Direction: In the following questions, the symbols @, $, #, © and % are used with the following meanings as illustrated below.
'P $ Q' means 'P is not smaller than Q'.
'P © Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means 'P is neither smaller than nor equal to Q'.
'P % Q' means 'P' is not greater than Q'.
'P @ Q' means 'P is neither greater than nor smaller than Q'.
Now, in each of the following questions assuming the given statements to be true, find which of the four Conclusions I, II, III and IV given below them is/are definitely true and given your answer accordingly.

Statements ::
D % A, A @ B, B © K, K % M
Conclusions ::
I. B $ D
II. K # A
III. M # B
IV. A © M

Statements ::
D % A ⇒ D ≤ A
A @ B ⇒ A = B
B © K ⇒ B < K
K % M ⇒ K ≤ M
i.e., D ≤ A = B < K ≤ M
Conclusions
I. B $ D ⇒ B ≥ D         (✔)
II. K # A ⇒ K > A         (✔)
III. M # B ⇒ M > B         (✔)
IV. A © M ⇒ A < M         (✔)

Correct Option: E

Statements ::
D % A ⇒ D ≤ A
A @ B ⇒ A = B
B © K ⇒ B < K
K % M ⇒ K ≤ M
i.e., D ≤ A = B < K ≤ M
Conclusions
I. B $ D ⇒ B ≥ D         (✔)
II. K # A ⇒ K > A         (✔)
III. M # B ⇒ M > B         (✔)
IV. A © M ⇒ A < M         (✔)
Hence, all Conclusion I, II, III and IV are definitely true.

Statements
F # H ⇒ F > H
H @ M ⇒ H = M
M © E ⇒ M < E
E $ J ⇒ E ≥ J
i.e., F > H = M < E ≥ J
Conclusions
I. J © M ⇒ J < M           (x)
II. E # H ⇒ E > H          (✔)
III. M © F ⇒ M < F        (✔)
IV. F # E ⇒ F > E            (x)
Hence, II and III are definitely true.

Correct Option: B

Statements
M @ B ⇒ M = B
B # N ⇒ B > N
N $ R ⇒ N ≥ R
R © K ⇒ R < K
i.e., M = B > N ≥ R < K
Conclusions
I. K # B ⇒ K > B          (x)
II. R © B ⇒ R < B         (✔)
III. M $ R ⇒ M ≥ R        (x)
IV. N © M ⇒ N < M       (✔)
Hence, II and IV are definitely true.