If A - p - q - r and B - x - y - find A - B-A- p- q-q- r-r- x-p- y-q- y-r- yB- -C- p- x-p- y-q- x-q- y-r- x-r- yD- x- x-p- x-q- x-r- x-y- y-p- y-q- y-r- y

The correct option is C (p,x), (p,y), (q,x), (q,y), (r,x), (r,y)Given, A = p,q,r and B = x,y A nbsp;× B = nbsp;p,q,r × x,y ∵ A × B = (a,b): a∈A and b∈B ⇒ A ...

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Byju's Answer

Standard X

Mathematics

Cartesian Product

If A = p , q ...

Question

If A = {p,q,r} and B = {x,y}, find A $\times$ B.

ϕ

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{(p,q) ,(q,r), (r,x), (p,y), (q,y), (r,y)}

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{(p,x), (p,y), (q,x), (q,y), (r,x), (r,y)}

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{(x,x), (p,x), (q,x), (r,x), (y,y), (p,y), (q,y), (r,y)}

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Solution

The correct option is C {(p,x), (p,y), (q,x), (q,y), (r,x), (r,y)}
Given, A = {p,q,r} and B = {x,y}
A $\times$ B = {p,q,r} $\times$ {x,y}
$∵$ A $\times$ B = {(a,b): a $\in$ A and b $\in$ B}
$\Rightarrow A \times B = (p, x), (p, y), (q, x), (q, y), (r, x), (r, y)$

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Similar questions

Q. Prove that the lines

(p - q) x + (q - r) y + (r - p) = 0

(q - r) x + (r - p) y + (p - q) = 0

(r - p) x + (p - q) y + (q - r) = 0

are concurrent.

Q. If

\frac{x}{q + r - p} = \frac{y}{r + p - q} = \frac{z}{p + q - r},

shew that (q - r)x + (r - p)y + (p - q) z = 0.

Q. If

a = x y^{p - 1}, b = x y^{q - 1}

and

c = x y^{r - 1},

prove that

a^{q - r} b^{r - p} c^{p - q} = 1

If a = $x y^{p - 1}, b = x y^{q - 1} a n d c = x y^{r - 1}$ , prove that $a^{q - r} b^{r - p} c^{p - q}$ = 1,

Q. If

∣ ∣ ∣ ∣ \begin{matrix} p & q - y & r - z p - x & q & r - z p - x & q - y & r \end{matrix} ∣ ∣ ∣ ∣ = 0

, then the value of

\frac{p}{x} + \frac{q}{y} + \frac{r}{z}

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If A = {p,q,r} and B = {x,y}, find A × B.

The correct option is C {(p,x), (p,y), (q,x), (q,y), (r,x), (r,y)}Given, A = {p,q,r} and B = {x,y} A × B = {p,q,r} × {x,y} ∵ A × B = {(a,b): a∈A and b∈B} ⇒A×B=(p,x),(p,y),(q,x),(q,y),(r,x),(r,y)

If A = {p,q,r} and B = {x,y}, find A $\times$ B.

The correct option is C {(p,x), (p,y), (q,x), (q,y), (r,x), (r,y)}
Given, A = {p,q,r} and B = {x,y}
A $\times$ B = {p,q,r} $\times$ {x,y}
$∵$ A $\times$ B = {(a,b): a $\in$ A and b $\in$ B}
$\Rightarrow A \times B = (p, x), (p, y), (q, x), (q, y), (r, x), (r, y)$