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Symbolise the following statements. Fo...

Symbolise the following statements.
For every real number x,x < x + 1.

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To symbolize the statement "For every real number x, x < x + 1", we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Universal Quantifier**: The phrase "For every" indicates that we are dealing with a universal quantifier. In mathematical notation, this is represented by the symbol ∀ (which means "for all"). 2. **Define the Variable**: We need to define the variable we are quantifying. In this case, the variable is x, which represents a real number. We denote this by writing \( x \in \mathbb{R} \), where \( \mathbb{R} \) represents the set of all real numbers. 3. **Express the Condition**: The condition we need to express is "x < x + 1". This is a straightforward inequality. 4. **Combine the Components**: We can now combine the universal quantifier, the variable definition, and the condition into a single expression. The complete symbolic representation will be: \[ \forall x \in \mathbb{R}, \, x < x + 1 \] ### Final Symbolized Statement: \[ \forall x \in \mathbb{R}, \, x < x + 1 \]
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