Tag: set language

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Multiple choice maths set language different sets de morgan's law de morgan's law for set theory

If $A=\left {x\epsilon C: x^2=1\right }$ and $B=\left {x\epsilon C: x^4=1\right }$, then $A\Delta B$ is equal to

  1. $\left \{-1, 1\right \}$
  2. $\left \{-1, 1, i, -i\right \}$
  3. $\left \{-i, i\right \}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x^2=1\Rightarrow x=-1, 1.\therefore A=\left {-1, 1\right }$
$x^4=1\Rightarrow x^2=-1, 1$
$\Rightarrow x=-i, i, -1, 1.\therefore B=\left {-i, i, -1, 1\right }$
$\therefore A\Delta B=(A-B)\cup (B-A)=\phi \cup \left {-i, i\right }=\left {-i, i\right }$.