Mathematics
Assertion (A) : If a polyhedron has 7 vertices and 10 faces, the number of edges is 19.
Reason (R) : The relationship between faces (F), edges (E) and vertices (V) of a polyhedron is F + V - E = 2.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
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Answer
By Euler's formula, the relationship between faces (F), edges (E) and vertices (V) of a polyhedron is : F + V - E = 2.
So, reason (R) is true.
Given,
V = 7 and F = 10
Substituting the values, in Euler's formula we get :
⇒ 10 + 7 - E = 2
⇒ 17 - E = 2
⇒ E = 17 - 2
⇒ E = 15
So, assertion (A) is false.
∴ A is false, but R is true.
Hence, option 4 is the correct option.
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