Explanation

The number of subsets of a set with n elements is 2^n.

Here, A = {a, b, c} has 3 elements, so:

Number of subsets = 2^3

= 8

The subsets are:

{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}

Explanation

The x-coordinate is negative and the y-coordinate is positive → (-1, √2).

This combination (−, +) always lies in Quadrant II.

Explanation

The square root of any real number is never negative, so √x = -10 has no real solution.

Hence, the solution set is empty, written as { }.

Explanation

Let's factor:

x^2 - y^2 = (x + y)(x - y)

x^2 - xy = x(x - y)

The common factor is (x - y).

Explanation

Given:

P(x) = x^2 - 4x + 3

One root is 1. Let's find the other root.

The sum of roots = -(-4) = 4 (from the coefficient of x)

One root is 1, so the other root would be:

4 - 1 = 3

Explanation

Explanation

قرآن کریم میں غزوہ تبوک کو "ساعۃ العسرۃ" یعنی تنگی و مشکل کا وقت کہا گیا ہے۔

یہ غزوہ سخت گرمی، قلتِ وسائل اور طویل سفر کے باوجود پیش آیا، اسی لیے اسے یہ لقب دیا گیا۔

Explanation

حضرت ابو بکر صدیق رضی اللہ عنہ نے نبی کریم صلی اللہ علیہ وسلم کی بیماری کے دوران نماز کی امامت کی۔

صحابہ کرام نے اسی کو خلافت کے لیے اہم دلیل قرار دیا، کیونکہ یہ نبی کی جانب سے ان پر اعتماد کی علامت تھی۔

Explanation

Personification is giving human qualities to non-human things — here, "stairs groaned" gives human action to stairs.

It creates imagery by making the object (stairs) seem alive.

Explanation

"For a common citizen" begins with the preposition "for" and ends with the noun "citizen", making it a prepositional phrase.

It shows the relationship between the obligation and who it applies to.