Home
Class 12
MATHS
Write the converse, inverse and contrapo...

Write the converse, inverse and contrapostitive to each of the following statements:
(a) if `x + 2 =6,` then ` x =4`
(b) If it is rainig, I stay at home
(c ) If A, B and C are the vectices of a triangle then `AB+ BCgt CA.`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of finding the converse, inverse, and contrapositive of the given statements, we will follow a systematic approach for each statement. ### (a) Statement: If \( x + 2 = 6 \), then \( x = 4 \) 1. **Identify p and q**: - Let \( p: x + 2 = 6 \) - Let \( q: x = 4 \) 2. **Converse**: - The converse of a statement "If p then q" is "If q then p". - **Converse**: If \( x = 4 \), then \( x + 2 = 6 \). 3. **Inverse**: - The inverse of a statement "If p then q" is "If not p then not q". - **Inverse**: If \( x + 2 \neq 6 \), then \( x \neq 4 \). 4. **Contrapositive**: - The contrapositive of a statement "If p then q" is "If not q then not p". - **Contrapositive**: If \( x \neq 4 \), then \( x + 2 \neq 6 \). ### (b) Statement: If it is raining, I stay at home. 1. **Identify p and q**: - Let \( p: \) It is raining. - Let \( q: \) I stay at home. 2. **Converse**: - **Converse**: If I stay at home, then it is raining. 3. **Inverse**: - **Inverse**: If it is not raining, then I do not stay at home. 4. **Contrapositive**: - **Contrapositive**: If I do not stay at home, then it is not raining. ### (c) Statement: If A, B, and C are the vertices of a triangle, then \( AB + BC > CA \). 1. **Identify p and q**: - Let \( p: \) A, B, and C are the vertices of a triangle. - Let \( q: \) \( AB + BC > CA \). 2. **Converse**: - **Converse**: If \( AB + BC > CA \), then A, B, and C are the vertices of a triangle. 3. **Inverse**: - **Inverse**: If A, B, and C are not the vertices of a triangle, then \( AB + BC \leq CA \). 4. **Contrapositive**: - **Contrapositive**: If \( AB + BC \leq CA \), then A, B, and C are not the vertices of a triangle. ### Summary of Results: - **(a)**: - Converse: If \( x = 4 \), then \( x + 2 = 6 \). - Inverse: If \( x + 2 \neq 6 \), then \( x \neq 4 \). - Contrapositive: If \( x \neq 4 \), then \( x + 2 \neq 6 \). - **(b)**: - Converse: If I stay at home, then it is raining. - Inverse: If it is not raining, then I do not stay at home. - Contrapositive: If I do not stay at home, then it is not raining. - **(c)**: - Converse: If \( AB + BC > CA \), then A, B, and C are the vertices of a triangle. - Inverse: If A, B, and C are not the vertices of a triangle, then \( AB + BC \leq CA \). - Contrapositive: If \( AB + BC \leq CA \), then A, B, and C are not the vertices of a triangle.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE)|7 Videos

  • MATHEMATICAL REASONING

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE) (LEVEL-II)|8 Videos

  • MATHEMATICAL REASONING

    FIITJEE|Exercise ILLUSTRATION|1 Videos

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise EXERCISE-8|1 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

Similar Questions

Explore conceptually related problems

" Write the converse of the statement if "x+2=6" then "x=4

If a, b, c are sides of a triangle, then ((a+b+c)^(2))/(ab+bc+ca) always belongs to

If the sines of the angle A and B of a triangle ABC satisfy the equation c^(2) x^(2) - c (a + b) x + ab = 0 , then the triangle

If a,b,c are the lengths of the sides of a triangle,then the range of (ab+bc+ca)/(a^(2)+b^(2)+c^(2))

Let ABC and A'B'C' be two triangles in which AB gt A'B', BC gt B'C' and CA gt C'A' . Let D, E and F be the midpoints of the sides BC, CA and AB respectively. Let D', E' and F' be the midpoints of the sides B'C', C'A' and A'B' respectively. Consider the following statements : Statement I: AD gt A'D', BE gt B'E' and CF gt C'F' are always true. Statement II : (AB^(2)+BC^(2)+CA^(2))/(AD^(2)+BE^(2)+CF^(2)) =(A'B'^(2)+B'C'^(2)+C'A'^(2))/(A'D'^(2) +B'E'^(2) +C'F'^(2)) Which one of the following is correct in respect of the above statements?