In this question on English idioms and phrases, you must select the option that best expresses the meaning of the idiom "the alpha and the omega", which is often used to talk about the complete extent of something.

Introduction / Context:
This question belongs to the topic of English idioms and phrases, which are fixed expressions whose meanings cannot always be guessed from individual words. The idiom given is "the alpha and the omega". It is frequently used in literature, speeches, and exams to describe the entire range or the first and last parts of something. Understanding such idioms is very important for scoring well in English sections of competitive examinations.

Given Data / Assumptions:
- The idiom in the question is "the alpha and the omega".
- The options are "Happy and sad", "The beginning and the end", "The love and the hatred", and "Truth and dare".
- Standard idiomatic usage in English is assumed.
- Only one option correctly gives the meaning of the idiom.

Concept / Approach:
The word "alpha" is the first letter of the Greek alphabet and "omega" is the last letter. When combined in the idiom "the alpha and the omega", they symbolically represent the beginning and the end of something, and by extension, sometimes the whole of it. When you see idioms that pair two extreme points, such as first and last, you should think of expressions like start and finish, source and conclusion, or the entirety of something.

Step-by-Step Solution:
Step 1: Recognise that "alpha" refers to the first letter and "omega" to the last letter of the Greek alphabet. Step 2: Understand that in idiomatic use, the phrase stands for the beginning and the end of something, and sometimes its full extent. Step 3: Evaluate "Happy and sad". This presents two opposite emotions, but does not capture the idea of beginning and end. Step 4: Evaluate "The beginning and the end". This directly matches the symbolic meaning of alpha and omega. Step 5: Evaluate "The love and the hatred" and "Truth and dare". These are just pairs of contrasting ideas and do not relate to start and finish.

Verification / Alternative check:
Many dictionaries and reference books explicitly define "the alpha and the omega" as "the beginning and the end" or "the first and the last". The other options are not recognised idiomatic meanings of this phrase. They contain contrasts, but the idiom itself is about extremes in terms of sequence, not emotional opposites. Therefore, "The beginning and the end" is the only accurate interpretation here.

Why Other Options Are Wrong:
"Happy and sad" is wrong because it deals with emotional states and is not linked to the concepts of starting and finishing. "The love and the hatred" is wrong because it again contrasts emotions. "Truth and dare" is wrong because it refers to a popular party game and has nothing to do with the alphabet or sequence. None of these match the established meaning of the idiom.

Common Pitfalls:
Students sometimes assume that if an idiom contains two nouns, it must be describing a pair of opposite feelings or qualities. This leads them to favour choices like "happy and sad" or "love and hatred". However, idioms often have historical or cultural roots, and their meanings must be learned as fixed expressions. The safest way is to remember that "alpha and omega" literally mark the first and last positions in a sequence, which naturally extends to the idea of the beginning and the end.

Final Answer:
The idiom "the alpha and the omega" means the beginning and the end.