search
Log In
0 votes
181 views

Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by

$$f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$$ Then $f(x, A \cup B)$ equals

  1. $f(x,A)+f(x,B)$
  2. $f(x,A)+f(x,B)\: – 1$
  3. $f(x,A)+f(x,B)\: – f(x,A) \cdot f(x,B)$
  4. $f(x,A)\:+ \mid f(x,A)\: – f(x,B) \mid $
in Set Theory & Algebra
recategorized by
181 views

Please log in or register to answer this question.

Related questions

0 votes
0 answers
1
172 views
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is non-empty none of the above
asked Sep 23, 2019 in Set Theory & Algebra Arjun 172 views
1 vote
2 answers
2
238 views
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
asked Sep 23, 2019 in Quantitative Aptitude Arjun 238 views
0 votes
2 answers
3
187 views
Suppose that a function $f$ defined on $\mathbb{R} ^2$ satisfies the following conditions: $\begin{array} &f(x+t,y) & = & f(x,y)+ty, \\ f(x,t+y) & = & f(x,y)+ tx \text{ and } \\ f(0,0) & = & K, \text{ a constant.} \end{array}$ Then for all $x,y \in \mathbb{R}, \:f(x,y)$ is equal to $K(x+y)$ $K-xy$ $K+xy$ none of the above
asked Sep 23, 2019 in Calculus Arjun 187 views
1 vote
1 answer
4
129 views
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x,$ for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
asked Sep 23, 2019 in Calculus Arjun 129 views
...