For the gate shown in the figure, the output will be HIGH

Step 1: Identify the gate type.
The given gate is an OR gate, which outputs HIGH if at least one of the inputs is HIGH.
Step 2: Analysis of options.
- (A) If and only if both the inputs are LOW: This is incorrect as the OR gate outputs LOW only when both inputs are LOW.
- (B) If and only if both the inputs are HIGH: This is incorrect since the OR gate will also output HIGH if just one input is HIGH.
- (C) If one of the inputs is HIGH: This is correct because the OR gate will output HIGH if either input is HIGH.
- (D) If one of the inputs is LOW: This is incorrect because the OR gate will still output HIGH if one input is HIGH.
Step 3: Conclusion.
The correct answer is (C), as the OR gate produces a HIGH output if one of the inputs is HIGH.
Find the least upper bound and greatest lower bound of \( S = \{X, Y, Z\} \) if they exist, of the poset whose Hasse diagram is shown below:
Suppose \( D_1 = (S_1, \Sigma, q_1, F_1, \delta_1) \) and \( D_2 = (S_2, \Sigma, q_2, F_2, \delta_2) \) are finite automata accepting languages \( L_1 \) and \( L_2 \), respectively. Then, which of the following languages will also be accepted by the finite automata:
(A) \( L_1 \cup L_2 \)
(B) \( L_1 \cap L_2 \)
(C) \( L_1 - L_2 \)
(D) \( L_2 - L_1 \)
Choose the correct answer from the options given below: