For the following question, consider the given mathematical statements to be true and determine which of the conclusions logically follow from them. Select the correct option accordingly.

Given Relationship:
$6779>5862<8241=5789$, $5789\ge 7145=3914$
Inferences:
I. $6779<5789$
II. $3914\ge 8241$

Correct Answer: Neither inference I nor II holds true

Step-by-Step Explanation:

Let us analyze the given mathematical relationships step by step.

Given Relationships:

1. $6779>5862<8241=5789$

2. $5789\ge 7145=3914$

Combining the expressions, we get the relationship chain:

$6779>5862<8241=5789\ge 7145=3914$

Analysis of Inference I:

Inference I states: $6779<5789$

From the combined relation between 6779 and 5789:

$6779>5862<8241=5789$

Notice that between 6779 and 5789, the signs are opposite (> and <). Therefore, no definite relationship can be established between 6779 and 5789.

Thus, Inference I does not follow.

Analysis of Inference II:

Inference II states: $3914\ge 8241$

From the given chain:

$8241=5789\ge 7145=3914$

This implies that $8241\ge 3914$, which means $3914\le 8241$.

Inference II claims $3914\ge 8241$, which is not definitely true (it could only be true if 3914 = 8241, but we cannot conclude greater than or equal to in that direction).

Thus, Inference II does not hold true.

Conclusion:

Neither inference I nor inference II holds true.