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Write the contrapositive and converse of the following statements.(i)      If x is a prime number, then x is odd.(ii)     If the two lines are parallel, then they do not intersect in the same plane, (iii)    Something is cold implies that it has low temperature.(iv)    You cannot comprehend geometry if you do not know how to reason deductively.(v)    x is an even number implies that x is divisible by 4.

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To solve the problem of writing the contrapositive and converse of the given statements, we will follow these steps: ### Step 1: Understand the Definitions 1. **Contrapositive**: For a statement "If P, then Q" (P → Q), the contrapositive is "If not Q, then not P" (¬Q → ¬P). 2. **Converse**: For the same statement "If P, then Q" (P → Q), the converse is "If Q, then P" (Q → P). ### Step 2: Write the Contrapositive and Converse for Each Statement ...
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Write the contrapositive of the following statements: (i)Something is cold implies that it has low temperature (ii)You cannot comprehend geometry if you do not know how to reason deductively.

Write the contrapositive of the following statements: (i)If x is prime number then x is odd (ii)If two lines re parallel then they do not intersect in the same plane. (iii) x is even number implies that x is divisible by 4.

Knowledge Check

  • The converse of the statement If two lines are parallel , then they do not intersect in the plane is

    A
    1. If two lines do not intersect in the same plane then they are parallel.
    B
    2. If two lines are not parallel then they do not intersect in the same plane.
    C
    3. If two lines are not parallel then they intersect in the same plane.
    D
    4. none of the above
  • The contrapositive of the statement If x is a prime number then x is odd is

    A
    1. If x is odd then x is a prime number.
    B
    2. If x is not a prime number then x is not odd .
    C
    3. If x is not odd then x is not a preme number.
    D
    4. If x is not then x is a prime number.
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