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Ex 14.5, 1 - Show that statement p: 'If x is a real number - Ex 14.5

Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 2
Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 3
Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 4
Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 5
Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 6
Ex 14.5, 1 - Chapter 14 Class 11 Mathematical Reasoning - Part 7

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Ex 14.5, 1 Show that the statement p: If x is a real number such that x3 + 4x = 0, then x is 0 is true by direct method The given statement is of the form if p then q Here p: x is a real number such that x3 + 4x = 0. q: x is 0 In direct method, we assume p is true, and prove q is true So, Let x be areal number such that x3 + 4x = 0, prove that x = 0 p is true Consider x3 + 4x = 0 where x is real x (x2 + 4) = 0 x = 4 is not possible because it is given that x is real. Hence x = 0 only q is true Hence proved Ex14.5, 1 Show that the statement p: If x is a real number such that x3 + 4x = 0, then x is 0 is true by (ii) method of contradiction, Method of contradiction p : if x is real number such that x3 + 4x = 0, then x is 0 Let us assume x3 + 4x = 0 but x 0 Solving x3 + 4x =0 x (x2 + 4 ) = 0 Or x = 4 is not possible because it is given that x is a real number Hence only solution is x = 0 but we take x 0 Hence we get a contradiction Hence our assumption is wrong Hence x is real number such that x3 + 4x = 0 then x is 0 Ex14.5, 1 Show that the statement p: If x is a real number such that x3 + 4x = 0, then x is 0 is true by (iii) method of contrapositive Method of Contrapositive Let p : If x is real . number such that x3 + 4x = 0 q : x is 0 The above statement is of the form if p then q Let q is false . i.e. x is not equal to 0 i.e. x 0 i.e. x (positive number) 0 (positive number) i.e. x (x2 + 4 ) 0 (x2 + 4) i.e. x3 + 4x 0 i.e. p is false.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.