To determine which language is accepted by the given deterministic finite automaton (DFA), we need to analyze the structure of the DFA and the transitions based on the states.

The DFA is defined over the alphabet Σ = {𝑎, 𝑏}. The task is to determine the language accepted by it from the given options.

Let's break down the transitions:

1. The initial state transitions on receiving 'a' or 'b'. Moving from state 1 to state 2 on 'b'.
2. From state 2, it remains in state 2 on 'b' and moves to state 3 on 'a'.
3. From state 3, it transitions back to state 2 on 'a' and moves to state 4 on 'b'.
4. From state 4, the final state, it returns to state 3 on 'a' and stays on state 4 on 'b'.

Now, let’s examine each option:

• The set of all strings containing an even number of 𝑏’s:
  This is not accepted because the DFA doesn't ensure even 𝑏's; the transitions don't reset based on the number of 𝑏's.
• The set of all strings containing the pattern 𝑏𝑎𝑏:
  The DFA does move through states on a 𝑏𝑎𝑏 pattern but doesn't end in a final state immediately after.
• The set of all strings ending with the pattern 𝑏𝑎𝑏:
  Correct Answer. The DFA reaches the final state precisely when the string ends with 𝑏𝑎𝑏.
• The set of all strings not containing the pattern 𝑎𝑏𝑎:
  There's no specific behavioral restriction on \( \text{ab}\text{a} \) pattern here.

Based on this analysis, the DFA accepts the set of all strings ending with the pattern 𝑏𝑎𝑏. Therefore, the correct answer is The set of all strings ending with the pattern 𝑏𝑎𝑏.