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In which scripture are the following verses found:

Aham brahmasmi
Meaning: I am Brahma

Shivoham
Meaning: I am Shiva

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The first one is an Vedantic verse taken from an upanishad. Another is probably non Vedic and appears in famous "NirvAna shatakam" stotra.

Tat Tvam Asi (Sanskrit: तत् त्वम् असि or तत्त्वमसि, "Thou art that," "That thou art," or "You are that") — is one of the Mahāvākyas (Grand Pronouncements).

It originally occurs in the Chandogya Upanishad 6.8.7, in the dialogue between Uddālaka and his son Śvetaketu; it appears at the end of a section, and is repeated at the end of the subsequent sections as a refrain. The meaning of this saying is that the Self - in its original, pure, primordial state - is wholly or partially identifiable or identical with the Ultimate Reality that is the ground and origin of all phenomena. The knowledge that this is so characterises the experience of liberation or salvation that accompanies the Unio Mystica.

Source

न च व्योम भूमिर्न तेजो न वायुः

चिदानन्दरूपः शिवोऽहम् शिवोऽहम् ॥१॥ Nirvana shatakam.

however, Soham and other similar phrases are found in yogic and agamic literature.

This sentence appears in the Brihadaranyaka Upanishad when the sage, in the context of meditation on the Self, in reply to the query – What did that Brahman know by which It became all? - states:-

"ब्रह्म वा इदमग्र आसीत्, तदात्मनामेवावेत्, अहं ब्रह्मास्मीति |

तस्मात्तत्सर्वमभवत्; तद्यो यो देवानां प्रत्यबुध्यत स एव तदभवत्, तदषीर्णाम् तथा मनुष्याणाम्,..."

"This (self) was indeed Brahman in the beginning; It knew only Itself as, "I am Brahman". Therefore It became all; and whoever among the gods knew It also became That; and the same with sages and men…” - (Brihadaranyaka Upanishad I.iv.10)

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There are multiple interpretations of these phrases.

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