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We draw the following table from given conditions:

Following symbols are used:

When the symbol A and B is interchanged we will proceed from the end side for better understanding.

We will check each option one by one: 

a) A*Q#N$X (X is the father of N, N is the mother of Q, Q is the sister of A)

clearly seen, X is the grandfather of A not grandmother. FALSE

b)  A@Q$N#X (X is the mother of N, N is the father of Q, Q is the husband of A)

Clearly seen, X is the grandmother of A's husband. FALSE

c)  A#Q$X*N (N is the sister of X, X is the father of Q, Q is the mother of A)

Clearly seen, X is the grandfather of A not grandmother. FALSE

d)  A#Q@N#X ( X is the mother of N, N is the husband of Q, Q is the mother of A)

Clearly seen, X is the grandmother of A. This is the correct relation. TRUE

Hence, A#Q@N#X is the correct option.

Decoding the information, 

Given:

208 D 113 B (5² D (6 B 4)) A 279 C 3 A 386 D 506

After replacing the signs from left to right and using the BODMAS rule,

= 208 – 113 × (5² - (6 × 4)) + 279 ÷ 3 + 386 – 506

= 208 – 113 × (25 - 24) + 279 ÷ 3 + 386 – 506

= 208 – 113 × 1 + 279 ÷ 3 + 386 – 506

= 208 – 113 × 1 + 93 + 386 – 506

= 208 – 113 + 93 + 386 – 506

= 687 – 113 – 506

= 687 – 619

= 68

Hence, “68” is the correct answer.

The water image of the given figure is:

Hence, the correct answer is "Option 4".

Important Points

• The reflection of an object into the water is its water image.
• It appears by inverting an object vertically i.e. upside down.
• The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Decoding the information, 

Given:

21 $ 7 M 13 < 2 R 6

After replacing the signs from left to right and using the BODMAS rule,

= 21 ÷ 7 + 13 - 2 × 6

= 3 + 13 - 2 × 6

= 3 + 13 – 12

= 16 – 12

= 4

Hence, “4” is the correct answer.

The logic followed here is as follows:

So, the next term is:

17 + 6 = 23

Hence, the correct answer is "23".

Preparing the family tree using the following symbols,

Given information –

1. M is daughter of R, who is not the father of M.

2. O and R are married couple

3. P is brother of O.

4. O is father of N.

We can draw the following Family Tree from the information given above:

Hence, M is sister of N.

The logic follows here is:-

Each 1^st letter is increasing by 4.

Each 2^nd letter is increasing by 5.

And each 3^rd letter is increasing by 6.

Hence, the correct answer is "FLQ".

Important Points

Concept:

1. We have to check the conclusions are 100% match with the statement. If the conclusion is 100% match with the given statement then the conclusion is true. If there is a 1% chance of not following the statement then the conclusion is considered to be false.

2. The possibility case can be considered to be "false" in "definite case".

3. In Possibility case, either "can" or "possible" word must be present.

The least possible venn diagram for the given statements is as follows:

Conclusions:

I. Some tigers are weird → False (It can be possible, but it is not definite)

II. All brave are tigers → False (It can be possible, but it is not definite)

III. No weird is tiger → False (It can be possible, but it is not definite)

But, conclusion I and III forms a complementary pair.

Hence, either conclusion I or III follows.

Note: 

Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Individually both the conclusions should be false.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Additional Information

From the given information,

 We can dram following Family Tree from information given above 

According to the given information:-

M % N & R % P @ L means M is married to N, N is brother of R, R is married to P, P is father of L.

The possible family tree diagram is

1. M is married to N

2. N is brother of R

3. R is married to P

4. P is father of L. So Final Family Tree is

Hence, N is the Uncle of L is the correct answer.

The relationship between "Apostate" and "Religion." An apostate is someone who renounces or abandons their religion. The key element of this relationship is the action of turning away from or betraying a fundamental belief or loyalty.

Now, let's analyze the given options:

1. Potentate : Kingdom - A potentate is a ruler or monarch of a kingdom; this pair signifies a position of authority over something rather than a betrayal or abandonment.

2) Teacher : Education - A teacher is an individual who imparts education or teaches. This pair indicates a role of providing or contributing to something rather than renouncing it.

3) Traitor : Country - A traitor is someone who betrays their country, typically by aiding an enemy. This relationship mirrors the notion of betrayal or abandonment inherent in the "Apostate : Religion" relationship.

4) Jailor : Law - A jailor is an individual who is in charge of a jail, responsible for overseeing prisoners. This relationship describes a custodial or overseeing role rather than abandonment or betrayal.

Given these analyses, the pair of words that bear the same relationship as "Apostate : Religion" is: Traitor : Country.

Hence, the correct answer is "Option 3".