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Frankl's UC sets conjecture states that for any nonempty UC family $\\mathcal{F} \\subseteq 2^{[n]}$ such that $\\mathcal{F} \\neq \\left\\{\\emptyset\\right\\}$, there exists an element $i \\in [n]$ that is contained in at least half the sets of $\\mathcal{F}$. The 3-sets conjecture of Morris states that the smallest number of distinct 3-sets (whose union is an $n$-set) that ensure Frankl's conjecture is satisfied for any UC family that contains them is $ \\lfloor{n/2\\rfloor} + 1$ for all $n \\geq 4$. 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