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An element <i>a</i> of a semigroup <i>S</i> is called a left [right] magnifier if there exists a proper subset <i>M</i> of <i>S</i> such that <inline-formula> <math display="inline"> <semantics> <mrow> <mi>a</mi> <mi>M</mi> <mo>=</mo> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>M</mi> <mi>a</mi> <mo>=</mo> <mi>S</mi> <mo>)</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> Let <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> denote the semigroup of all transformations on a nonempty set <i>X</i> under the composition of functions, <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">P</mi> <mo>=</mo> <mo>{</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>∣</mo> <mi>i</mi> <mo>∈</mo> <mi mathvariant="sans-serif">Λ</mi> <mo>}</mo> </mrow> </semantics> </math> </inline-formula> be a partition, and <inline-formula> <math display="inline"> <semantics> <mi>ρ</mi> </semantics> </math> </inline-formula> be an equivalence relation on the set <i>X</i>. In this paper, we focus on the properties of magnifiers of the set <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mi>f</mi> <mo>∈</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>∣</mo> <mo>∀</mo> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>∈</mo> <mi>ρ</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>x</mi> <mi>f</mi> <mo>,</mo> <mi>y</mi> <mi>f</mi> <mo>)</mo> </mrow> <mo>∈</mo> <mi>ρ</mi> <mspace width="4.pt"></mspace> <mi>and</mi> <mspace width="4.pt"></mspace> <msub> <mi>X</mi> <mi>i</mi> </msub> <mi>f</mi> <mo>⊆</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mspace width="4.pt"></mspace> <mi>for</mi> <mspace width="4.pt"></mspace> <mi>all</mi> <mspace width="4.pt"></mspace> <mi>i</mi> <mo>∈</mo> <mi mathvariant="sans-serif">Λ</mi> <mo>}</mo> </mrow> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> which is a subsemigroup of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mo>(</mo> <mi>X</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> and provide the necessary and sufficient conditions for elements in <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> to be left or right magnifiers.