Question

What are the true and false statements for If two planes intersect, then their intersection is a line. Include converse, inverse and contrapositive.

Answer 1

Answer and Step-by-step explanation:

Solution:

Statement:

If two planes intersect  their intersection is a line.

Suppose that

P =if two planes intersect.

q = then their intersection is line.

¬p = if two planes do not intersect.

¬q = then their intersection is not a line.

Converse:

If two planes intersect their intersection is a line.

P → q

Inverse:

If two planes do not intersect, then their intersection is not a line.

¬p → ¬q

Contrapositive:

If two planes intersection is not a line, then they do not intersect.

¬q → ¬p