Word Count : 554

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यहां पर \( X = \mathbb{R} \setminus \{-1\} \) और ऑपरेटर \( * \) परिभाषित किया गया है: \[ X_1 * X_2 = X_1 + X_2 + X_1 X_2, \quad \forall X_1, X_2 \in X \] अब हमें दो प्रश्नों का उत्तर देना है: ### i) क्या \( (X, *) \) एक समूह है? एक समूह (group) होने के लिए निम्नलिखित शर्तें पूरी होनी चाहिए: 1. संलग्नता (Associativity): \((X, *)\) पर ऑपरेशन संलग्न होना चाहिए। यानी, हमें यह साबित करना होगा कि \( (X_1 * X_2) * X_3 = X_1 * (X_2 ____ ______ _________ _______ __________ ____ ______ _________.
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