How to type symbols and commands (opens to a new tab)

You can copy and use some difficult-to-type symbols below:

Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω
α β γ δ ε ζ η θ ι κ λ μ ν ξ π ρ σ τ υ φ χ ψ ω ϑ ϕ ϵ
¬ ∧ ∨ ← → ↔ ↠ ⇐ ⇒ ⇔ ∀ ∃
− ⋅ √ ⌈ ⌉ ⌊ ⌋ ≠ ≡ ≤ ≥

Propositional logic exercise

Prove that `harr` is associative. Start with `(P harr Q) harr R` and proceed in logically equivalent steps. MathCheck will only check that your input doesn't contain errors, and not that your final step is reasonable. MathCheck also already knows that `harr` is associative, so use #( and #) to force printing the parentheses.

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