Question :
Option :
-
Father’s sister
-
Wife’s sister
-
Daughter
-
Wife
correct answer : a)
First, let’s clearly understand what each symbol means:
1. **I × J**: “I is the mother of J”
2. **I + J**: “I is the husband of J”
3. **I ÷ J**: “I is the sister of J”
4. **I – J**: “I is the brother of J”
### Analyzing the Expression: Q ÷ X + Y × Z
The expression is `Q ÷ X + Y × Z`. To interpret this correctly, we need to consider the order of operations. In mathematics, multiplication and division have higher precedence than addition, but here, since these are custom operations, we’ll assume the expression is to be read from left to right unless parentheses indicate otherwise. However, typically in such problems, operations are applied in the order they appear unless specified.
But looking at the options and the structure, it’s more likely that the expression is grouped as `(Q ÷ X) + (Y × Z)`. That is, first `Q ÷ X`, then `Y × Z`, and then combine the two with `+`.
Let’s break it down:
1. **Q ÷ X**: “Q is the sister of X”
2. **Y × Z**: “Y is the mother of Z”
3. **(Q ÷ X) + (Y × Z)**: Now, we’re combining these two with `+`, which means “is the husband of”.
So, `(Q ÷ X) + (Y × Z)` would mean “(Q is the sister of X) is the husband of (Y is the mother of Z)”.
This seems a bit convoluted. Maybe it’s better to think of it as:
– `A + B` means “A is the husband of B”. Here, `A` is `Q ÷ X` and `B` is `Y × Z`.
– So, “Q ÷ X is the husband of Y × Z”.
Now, let’s substitute the meanings:
– “Q is the sister of X” is the husband of “Y is the mother of Z”.
This implies that “Q is the sister of X” is married to “Y is the mother of Z”.
But “Q is the sister of X” is a person (Q), and “Y is the mother of Z” is also a person (Y). So, Q is the sister of X, and Q is the husband of Y, who is the mother of Z.
Wait, but if Q is the sister of X, Q is female (since sister implies female). But then Q cannot be the husband of Y, because husband implies male. This seems contradictory.
Perhaps I misinterpreted the grouping. Maybe the expression is to be read as `Q ÷ (X + (Y × Z))`. Let’s try that.
Alternative grouping: `Q ÷ (X + (Y × Z))`
1. `Y × Z`: “Y is the mother of Z”
2. `X + (Y × Z)`: “X is the husband of (Y is the mother of Z)”, meaning “X is the husband of Y”, and Y is the mother of Z.
– So, X is married to Y, and Y is the mother of Z. Therefore, X is the father of Z.
3. `Q ÷ (X + (Y × Z))`: “Q is the sister of (X is the husband of Y is the mother of Z)”, which simplifies to “Q is the sister of X”, and we know X is the father of Z.
– So, Q is the sister of X, who is the father of Z. Therefore, Q is the aunt of Z.
But looking at the options:
1. Father’s sister
2. Wife’s sister
3. Daughter
4. Wife
“Aunt” would correspond to “father’s sister”, which is option 1.
But let me re-examine the initial grouping because the first interpretation led to a contradiction (Q being both sister and husband). The second grouping seems more plausible because it avoids the contradiction and fits one of the options.
### Verifying the Grouping
Given that the first grouping led to a contradiction (Q being both sister and husband), it’s likely that the intended grouping is the second one: `Q ÷ (X + (Y × Z))`.
So, step-by-step:
1. `Y × Z`: Y is the mother of Z.
2. `X + (Y × Z)`: X is the husband of Y (since Y is the mother of Z, this makes X the father of Z).
3. `Q ÷ (X + (Y × Z))`: Q is the sister of X.
– Since X is the father of Z, Q is the sister of Z’s father, making Q the paternal aunt of Z, or “father’s sister”.
### Checking the Options
The options are:
1. Father’s sister
2. Wife’s sister
3. Daughter
4. Wife
Our conclusion is that Q is the “father’s sister” of Z, which is option 1.
### Final Answer
**1. Father’s sister**
### Summary
– `Y × Z`: Y is the mother of Z.
– `X + (Y × Z)`: X is the husband of Y → X is the father of Z.
– `Q ÷ (X + (Y × Z))`: Q is the sister of X → Q is the father’s sister of Z.
Thus, Q is Z’s **father’s sister**.