Given the following statements: - $L I = N P$ - $I \geq R K$ - $N \leq E P$ II. $R N$ II. $I

Question

Given the following statements: - $L > I = N > P$ - $I \geq R > K$ - $N \leq E < Z$ Determine the truth of the conclusions below: 6. Conclusions: I. $E > P$ II. $R < L$ 7. Conclusions: I. $K > N$ II. $I < Z$ Choose the correct option: (a) If only conclusion I is true. (b) If only conclusion II is true. (c) If either conclusion I or II is true. (d) If neither conclusion I nor II is true. (e) If both conclusions I and II are true.

Accepted Answer

**Solution:** We analyze the given statements and conclusions step-by-step. ### Given Statements: 1. $L > I = N > P$ 2. $I \geq R > K$ 3. $N \leq E < Z$ --- ### For Question 6: **Conclusions:** I. $E > P$ II. $R < L$ - From statement 1: $L > I = N > P$ implies $L > I$, $I = N$, and $N > P$. - From statement 3: $N \leq E < Z$ implies $E$ is greater than or equal to $N$ and less than $Z$. Since $N > P$ and $E \geq N$, it follows that $E > P$ or $E = N > P$. So conclusion I ($E > P$) is **true**. From statement 2: $I \geq R$ and from statement 1: $L > I$, so $L > I \geq R$ which implies $L > R$. Hence, $R < L$ is **true**. Thus, **both conclusions I and II are true** for question 6. --- ### For Question 7: **Conclusions:** I. $K > N$ II. $I < Z$ - From statement 2: $I \geq R > K$ implies $I > K$ or $I = R > K$, so $K < I$. - From statement 1: $I = N$, so $K < N$. Therefore, conclusion I ($K > N$) is **false**. - From statement 3: $N \leq E < Z$ and $I = N$, so $I \leq E < Z$ which means $I < Z$ or $I = E < Z$. Hence, conclusion II ($I < Z$) is **true**. So for question 7, only conclusion II is true. --- **Answer:** - For question 6: (e) Both conclusions I and II are true. - For question 7: (b) Only conclusion II is true.

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