Home
Class 12
MATHS
If x in A " and " A cancelsub B, " then...

If `x in A " and " A cancelsub B, " then " x in B`. Is this statement true ?

Text Solution

AI Generated Solution

To determine whether the statement "If \( x \in A \) and \( A \nsubseteq B \), then \( x \in B \)" is true or false, we can analyze the statement step by step. ### Step-by-Step Solution: 1. **Understanding the Statement**: - The statement claims that if an element \( x \) is in set \( A \) and set \( A \) is not a subset of set \( B \), then \( x \) must also be in set \( B \). - We need to check if this conclusion logically follows from the premises. ...
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE ENGLISH|Exercise Solved Exp|11 Videos
  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 1.1|12 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos
  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If A sub B "and " C, " then " A in C is this statement true ?

If A cancelsub B " and " B cancelsub C .Is this statement true ? A is not subset of C

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.(i) If x in A a n d A in B , t h e n x in B (ii) If A sub B a n d B in C then A in C

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If (log)_(((log)_5x))5=2,\ t h n\ x=5^(sqrt(5)) Statement II: (log)_x a=b ,\ if\ a >0,\ t h e n\ x=a^(1//b) a. A b. \ B c. \ C d. D

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) a. A b. \ B c. \ C d. D

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If A is obtuse angle I A B C , then tanB\ t a n C<1 because Statement II: In A B C ,\ t a n A=(t a n B+t a n C)/(t a n B t a n C-1)\ a. A b. \ B c. \ C d. D

Statement I is True: Statement II is True; Statement II is a correct explanation for statement I Statement I is true, Statement II is true; Statement II not a correct explanation for statement I. Statement I is true, statement II is false Statement I is false, statement II is true Statement I: if r ,\ s\ &\ t be the roots of the equation : x(x-2)(3x-7)=2,\ t h e ntan^(-1)r+tan^(-1)s+tan^(-1)t=3pi//4 because Statement II: The roots of the equation x(x-2)(3x-7)=2 are real & negative. a. A b. \ B c. \ C d. D

Statement I is True: Statement II is True; Statement II is a correct explanation for statement I Statement I is true, Statement II is true; Statement II not a correct explanation for statement I. Statement I is true, statement II is false Statement I is false, statement II is true Statement I: Range of cos(sec^(-1)(1/x)+cos e c1/xtan^(-1)x)i s\ [-1/(sqrt(2)),1/(sqrt(2))] because Statement II: Range of sin^(-1)x+tan^(-1)x+cos^(-1)x\ i s\ [pi/4,(3pi)/4] a. A b. \ B c. \ C d. D

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If s intheta+cos e ctheta=2,\ t h e nsin^ntheta=cos e c^ntheta=2^n because Statement II: If \ a+b=2,\ a b=1, then a=b=1\ a. A b. \ B c. \ C d. D

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: cos^3alpha+cos^3(alpha+(2pi)/3)+(alpha+(4pi)/3)=2cosalphacos(alpha+(2pi)/3)cos(alpha+(4pi)/3) because Statement II: In a+b+c=0=>a^3+b^3+c^3=3a c a. A b. \ B c. \ C d. D