Mathematical Reasoning

If the statement "If it rains, then the ground is wet" is true, which of the following is its contrapositive?

Which of the following statements is a tautology?

Given the statements: p: "I study", q: "I pass", which of the following represents the implication "If I study, then I pass"?

If the statement "All Indians are hardworking" is true and "Some hardworking people are doctors" is true, which of the following conclusions is logically valid?

Which of the following is the negation of the statement: "For every x in R, x² ≥ 0"?

Consider the statements: p: "It is sunny", q: "I will go to the park". Which compound statement is logically equivalent to ¬p ∨ q?

In a certain town, the statement "If a person is a teacher, then the person is educated" is true. Which of the following is the inverse of this statement?

Which of the following represents the converse of the statement "If a number is divisible by 4, then it is even"?

If p and q are statements, which of the following is logically equivalent to ¬(p ∧ q)?

Given two statements p and q, which of the following is a valid inference rule?