## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

1. Statements
H < J,
F < H,
I ≤ J = K
Conclusions
I. H > I
II. I ≥ F

1. Given that,
H < J .....(i)
F < H .....(ii)
I ≤ J = K ......(iii)
On combining the statement (i), (ii) and (iii), we get
F < H < J = K ≥ I
Conclusions
I. H > I (false)
II. I ≥ F (false)

##### Correct Option: D

Given that,
H < J ..............(i)
F < H ..............(ii)
I ≤ J = K ......(iii)
On combining the statement (i), (ii) and (iii), we get
F < H < J = K ≥ I
Conclusions
I. H > I (false)
II. I ≥ F(false)
So, it is clear that neither Conclusion i nor II follows the given statements.

1. Statements
A < B < C ≤ D = E
Conclusions
I. B ≤ E
II. B < E

1. Given that,
A < B < C ≤ D = E
Conclusions
I. B ≤ E       (false)
II. B < E       (true)

##### Correct Option: E

Given that,
A < B < C ≤ D = E
Conclusions
I. B ≤ E       (false)
II. B < E       (true)
So, it is clear that only Conclusion II follow from the given statements.

1. Statements
P > M > Q,
Q > Z > N
Conclusions
I. M ≥ Z
II. N < P

1. Given that,
i. P > M > Q
ii. Q > Z > N
On combining the statement (i) and (ii) we get
P > M > Q > Z > N
Conclusions
I. M ≥ Z       (false)
II. N < P       (true)

##### Correct Option: B

Given that,
i. P > M > Q
ii. Q > Z > N
On combining the statement (i) and (ii) we get
P > M > Q > Z > N
Conclusions
I. M ≥ Z       (false)
II. N < P       (true)
So, it is clear that only Conclusion II follows from the given statements.

1. Which of the following expression will be true, if the given expression K ≥ G > H ≤ F is definitely true ?

1. Now, we can check all the options one by one
(a) F ≥ K
Given equation,
1. K ? G > H ? F
Then relation between F and K will be from 1,
2. K ? H ? F (cannot decide between K and F)

(b) H < K
from 1. Relation between H and K will be
3. K ? G > H
from 3
H < K

(c) F < G
Relation between F and G from 1,
G > H ? F (cannot decide between G and F)

(d) K ≥ H
Relation Between K and H,
From 1. K ? G > H means K > H

##### Correct Option: B

Now, we can check all the options one by one
(a) F ≥ K......(false)
(b) H < K .......(true)
(c) F < G ......(false)
(d) K ≥ H ......(false)
So, it clear that option (b) true ,

1. In which of the following expression will the expression ' A < D' be definitely true ?

1. Try all option one by one.

##### Correct Option: C

Try all option one by one.
From the expression "C "--
A < B = C ≤ D,
A < D will be definitely true .