This question tests your knowledge of commonly confused words, specifically homophones or words that sound similar but have different meanings and spellings. To accurately complete the sentence, we need to choose the words that fit both grammatically and contextually.

Understanding 'Bear' vs. 'Bare'

Let's first look at the difference between 'bear' and 'bare':

• Bear: As a verb, 'bear' means to tolerate, to carry, or to endure something. For example, "She couldn't bear the heat." or "He was asked to bear the responsibility."
• Bare: As a verb, 'bare' means to uncover or expose. As an adjective, 'bare' means uncovered, naked, or empty. For example, "He decided to bare his soul." or "The trees were bare in winter."

In the sentence fragment "She could not _____ the thought of...", the meaning implies enduring or tolerating a thought. Therefore, 'bear' is the correct choice here.

Understanding 'Losing' vs. 'Loosing'

Now, let's differentiate between 'losing' and 'loosing':

• Losing: This is the present participle of the verb 'lose'. 'Lose' means to fail to win, to misplace, or to no longer have something. For example, "He is always losing his keys." or "Our team is losing the game."
• Loosing: This is the present participle of the verb 'loose'. 'Loose' (as a verb) means to set free, to unfasten, or to release. For example, "The farmer was loosing the sheep from the pen." or "He was loosing the knots on the rope."

In the sentence fragment "...of _________ the election to her bitter rival", the context is about the outcome of an election where one side does not win. This clearly points to 'losing' (failing to win) as the appropriate word.

Applying Words to the Sentence Context

Let's apply these definitions to the given sentence: "She could not _____ the thought of _________ the election to her bitter rival."

For the first blank:

• "She could not bear the thought..." means she could not tolerate or endure the idea. This fits the context perfectly.
• "She could not bare the thought..." would mean she could not expose or uncover the thought, which does not make sense in this context.

For the second blank:

• "...of losing the election..." means failing to win the election. This is the standard phrase used for election outcomes.
• "...of loosing the election..." would mean setting the election free or unfastening it, which is nonsensical.

Identifying the Correct Pair

Based on our analysis, the only pair that logically and grammatically completes the sentence is "bear, losing". Let's look at the options:

The pair bear and losing correctly completes the sentence to mean "She could not tolerate the thought of failing to win the election to her bitter rival."