Answer :
Certainly! Let's analyze the given conditional statement [tex]\((5 = 5) \rightarrow (4 = 3)\)[/tex].
### Step-by-Step Solution:
1. Identify the Components of the Conditional Statement:
- [tex]\((5 = 5)\)[/tex]: This is the antecedent or the "if" part of the statement.
- [tex]\((4 = 3)\)[/tex]: This is the consequent or the "then" part of the statement.
2. Evaluate the Antecedent:
- The statement [tex]\(5 = 5\)[/tex] is a true statement because 5 is indeed equal to 5.
3. Evaluate the Consequent:
- The statement [tex]\(4 = 3\)[/tex] is a false statement because 4 is not equal to 3.
4. Understand the Implication ([tex]\(\rightarrow\)[/tex]):
- In logic, an implication [tex]\(p \rightarrow q\)[/tex] (read as "if [tex]\(p\)[/tex], then [tex]\(q\)[/tex]") is false only when [tex]\(p\)[/tex] is true and [tex]\(q\)[/tex] is false. In all other cases, the implication is true.
5. Apply the Logical Implication:
- Here [tex]\(p\)[/tex] is [tex]\(5 = 5\)[/tex] and [tex]\(q\)[/tex] is [tex]\(4 = 3\)[/tex].
- Since [tex]\(5 = 5\)[/tex] is true and [tex]\(4 = 3\)[/tex] is false, we are in the case where the antecedent is true and the consequent is false.
By the definition of logical implication, if the antecedent is true and the consequent is false, the entire conditional statement is false.
### Conclusion:
Therefore, the conditional statement [tex]\((5 = 5) \rightarrow (4 = 3)\)[/tex] is false.
### Step-by-Step Solution:
1. Identify the Components of the Conditional Statement:
- [tex]\((5 = 5)\)[/tex]: This is the antecedent or the "if" part of the statement.
- [tex]\((4 = 3)\)[/tex]: This is the consequent or the "then" part of the statement.
2. Evaluate the Antecedent:
- The statement [tex]\(5 = 5\)[/tex] is a true statement because 5 is indeed equal to 5.
3. Evaluate the Consequent:
- The statement [tex]\(4 = 3\)[/tex] is a false statement because 4 is not equal to 3.
4. Understand the Implication ([tex]\(\rightarrow\)[/tex]):
- In logic, an implication [tex]\(p \rightarrow q\)[/tex] (read as "if [tex]\(p\)[/tex], then [tex]\(q\)[/tex]") is false only when [tex]\(p\)[/tex] is true and [tex]\(q\)[/tex] is false. In all other cases, the implication is true.
5. Apply the Logical Implication:
- Here [tex]\(p\)[/tex] is [tex]\(5 = 5\)[/tex] and [tex]\(q\)[/tex] is [tex]\(4 = 3\)[/tex].
- Since [tex]\(5 = 5\)[/tex] is true and [tex]\(4 = 3\)[/tex] is false, we are in the case where the antecedent is true and the consequent is false.
By the definition of logical implication, if the antecedent is true and the consequent is false, the entire conditional statement is false.
### Conclusion:
Therefore, the conditional statement [tex]\((5 = 5) \rightarrow (4 = 3)\)[/tex] is false.
