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Which pairs of statements are logically equivalent? Check all that apply.
the inverse and the contrapositive of the original conditional statement
the original conditional statement and its contrapositive
the original conditional statement and its inverse
the converse and the inverse of the original conditional statement
the converse and the contrapositive of the original conditional statement

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rgwoot
Which pairs of statements are logically equivalent? Check all that apply.
NO, the inverse and the contrapositive of the original conditional statement
☆Yes,the original conditional statement and its contrapositive
NO, the original conditional statement and its inverse
☆YES, the converse and the inverse of the original conditional statement
NO, the converse and the contrapositive of the original conditional statement

Answer :

The statement which logically equivalent: the original conditional statement and its contrapositive, the converse and the inverse of the original conditional statement.

Explanation :

Let the original statement be [tex]O\rightarrow P[/tex]. Then converse becomes [tex]P\rightarrow O[/tex].

Inverse is [tex]not O\rightarrow not P[/tex] then Contra positive is [tex]not P\rightarrow not O[/tex].

Further Explanation :

A conditional statement is given everywhere either in subject of mathematics or elsewhere. However, it is important to take care of the changed position of Q, P, which should have the same negation as the conditional statement, has in the form of “If P then Q”. Thus, we get 3 new conditional statements, named as contra positive, inverse, and converse.

Consider, the original statement “If you catch the ball, you can play”.

Contra positive:

  • If you can not play, then you do not catch the ball.

Inverse:

  • If you do not catch the ball, you can not play.

Converse:  

  • If you can play, then catch the ball.

Thus, we say, the original statement and its contra positive are logically equivalent,

  • The converse of the inverse and converse of the original statement are logically equivalent.  

Learn More:  

https://brainly.com/question/7066208 ,  Answered by Andriansp

Logical equivalent:  https://brainly.com/question/13421248 , Answered by ColinJacobus

Keywords :

Logically equivalent, contra positive, inverse, converse.

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