Question

If \(H<G=J\) and \(J>K\), then which of the following is necessarily true?
(I) \(H>K\)
(II) \(G>K\)

• A. only (I) is true.
• B. Neither (I) nor (II) are true.
• C. only (II) is true.
• D. both (I) and (II) are true.

Hint:

When a chain includes equality, substitute it directly: \(G=J\) and \(J>K \Rightarrow G>K\). Be careful—\(H<G\) does not compare \(H\) and \(K\) definitively.

Answer 1

The Correct Option is D

Given \(H < G = J\) and \(J > K\).  

From \(G = J\) and \(J > K\) \(\Rightarrow\) \(G > K\) is certain. 

About (I): We only know \(H < G\) and \(G > K\). This does not force \(H > K\); it is possible that \(H \leq K\) or \(H > K\) depending on actual values. 

\(\Rightarrow\) (I) is not necessary, but (II) is necessary. 

\(\boxed{\text{Only (II) is true}}\)