1.Set Theory
easy

किन्हीं भी समुच्चयों $A$ तथा $B$ के लिए, क्या यह सत्य है कि $P ( A ) \cup P ( B )= P ( A \cup B ) ?$ अपने उत्तर का औचित्य बताइए

Option A
Option B
Option C
Option D

Solution

False

Let $A=\{0,1\}$ and $B =\{1,2\}$

$\therefore A \cup B=\{0,1,2\}$

$P(A)=\{\varnothing,\{0\},\{1\},\{0,1\}\}$

$P(B)=\{\varnothing,\{1\},\{2\},\{1,2\}\}$

$P(A \cup B)=\{\varnothing,\{1\},\{2\},\{0,1\},\{1,2\},\{0,2\},\{0,1,2\}\}$

$P(A) \cup P(B)=\{\varnothing,\{1\},\{0,1\},\{2\},\{1,2\}\}$

$P(A) \cup P(B)=\{\varnothing,\{1\},\{0,1\},\{2\},\{1,2\}\}$

$\therefore P(A) \cup P(B) \neq P(A \cup B)$

Standard 11
Mathematics

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