Question

Prove that for every \( x, y \in \mathbb{R} \), if \( x+y \geq 100 \) then \( x \geq 50 \) or \( y \geq 50 \). Let \( x, y \in Z \). Prove that if \( a \) divides \( b \) and \( a \) divides \( c \) then \( a \) divides \( b x+c y \). Let \( a, b, c, d \in \mathbb{Z}^{+} \). Prove that if \( a \) divides \( b \) and \( c \) divides \( d \) then \( a c \) divides \( b d \). Let \( a, b \) and \( c \) be positive integers. Prove that if \( a \) divides \( b c \) then \( a \) divides \( b \) or \( a \) divides \( c \).

          Prove that for every \( x, y \in \mathbb{R} \), if \( x+y \geq 100 \) then \( x \geq 50 \) or \( y \geq 50 \).
Let \( x, y \in Z \). Prove that if \( a \) divides \( b \) and \( a \) divides \( c \) then \( a \) divides \( b x+c y \).
Let \( a, b, c, d \in \mathbb{Z}^{+} \). Prove that if \( a \) divides \( b \) and \( c \) divides \( d \) then \( a c \) divides \( b d \).
Let \( a, b \) and \( c \) be positive integers. Prove that if \( a \) divides \( b c \) then \( a \) divides \( b \) or \( a \) divides \( c \).

Prove that for every x, y ∈ℝ, if x+y ≥ 100 then x ≥ 50 or y ≥ 50.
Let x, y ∈ Z. Prove that if a divides b and a divides c then a divides b x+c y.
Let a, b, c, d ∈ℤ^+. Prove that if a divides b and c divides d then a c divides b d.
Let a, b and c be positive integers. Prove that if a divides b c then a divides b or a divides c.

Added by Selasi J.

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