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The correct answer is option 3 - INCITE.
Let`s analyze each option to understand why the other options are not correct:
Option 1 - SCIENCE: This word cannot be formed using the letters from INTELLIGENCE, as it contains the letter "S" which is not present in INTELLIGENCE.
Option 2 - NOTICE: This word cannot be formed using the letters from INTELLIGENCE because it contains the letter "O" which is not present in INTELLIGENCE.
Option 4 - ENTAIL: This word cannot be formed using the letters from INTELLIGENCE because it contains the letter "A" which is not present in INTELLIGENCE.
Option 3 - INCITE: This is the correct answer. All the letters needed to form the word INCITE can be found within the letters of INTELLIGENCE.
Therefore, the correct answer is option 3 - INCITE.