If p and q are two logical statements and A and B are two sets, then `p to q` corresponds to

Options

A. `A sube B`
B. `A cap B`
C. ` A cup B`
D. ` A cancelsube B`

Answer

To solve the problem, we need to understand the logical implication and its correspondence in set theory.

### Step-by-Step Solution:

1. **Understanding Logical Implication**:
The statement "p implies q" (denoted as \( p \to q \)) means that if \( p \) is true, then \( q \) must also be true. In logical terms, this can be expressed as:
- If \( p \) is true, \( q \) is true.
- If \( p \) is false, \( q \) can be either true or false.

2. **Correspondence to Sets**:
In set theory, if we have two sets \( A \) and \( B \), the statement "A is a subset of B" (denoted as \( A \subseteq B \)) means that every element of set \( A \) is also an element of set \( B \).

3. **Relating Logical Implication to Sets**:
The logical implication \( p \to q \) can be interpreted in terms of sets as follows:
- If \( p \) corresponds to the set \( A \) and \( q \) corresponds to the set \( B \), then the implication \( p \to q \) implies that if an element belongs to set \( A \) (i.e., \( p \) is true), it must also belong to set \( B \) (i.e., \( q \) is true).
- This relationship indicates that set \( A \) is a subset of set \( B \).

4. **Conclusion**:
Therefore, the logical statement \( p \to q \) corresponds to the set relationship \( A \subseteq B \).

### Final Answer:
The correct correspondence is that \( p \to q \) corresponds to \( A \subseteq B \).