Write the converse of the following true conditional statement. If the converse is false, write a counterexample.
If x less-than 20, then x less-than 30.
If x less-than 30, then x less-than 20; true.
If Image with alt text: x less-than 30 , then Image with alt text: x less-than 20 ; true.
If x less-than 30, then x less-than 20; false.
Counterexample: x = 27 and x greater-than 20.
If Image with alt text: x less-than 30 , then Image with alt text: x less-than 20 ; false. Counterexample: x = 27 and Image with alt text: x greater-than 20 .
If x greater-than 20, then x greater-than 30; false.
Counterexample: x = 25 and x less-than 30.
If Image with alt text: x greater-than 20 , then Image with alt text: x greater-than 30 ; false. Counterexample: x = 25 and Image with alt text: x less-than 30 .
If x greater-than 30, then x greater-than 20; true.
If x greater-than 20, then x greater-than 30; true.
Is this correct
No, that is incorrect. The converse of the statement "If x less-than 20, then x less-than 30" is "If x less-than 30, then x less-than 20".
is this correct
Yes, my apologies for the confusion. The converse of the statement "If x less-than 20, then x less-than 30" is indeed "If x less-than 30, then x less-than 20". Thank you for pointing that out.
The converse of the given conditional statement is: "If x less-than 30, then x less-than 20."
However, the converse is false. A counterexample is when x = 27. In this case, x is less than 30 but not less than 20. Therefore, the statement "If x less-than 30, then x less-than 20" is not true.
If x greater-than 30, then x greater-than 20; true.
If Image with alt text: x greater-than 30 , then Image with alt text: x greater-than 20 ; true.