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A grocery shop gives offer to the customers for specific products purchased. The products considered for giving offer are bar chocolate, cookie, and cake. While billing, first the bar chocolates are customers if the number of the cakes billed is equivalent to thrice the number of bar chocolates The customers can purchase in many ways subject to the above restrictions For example: 3 bar chocolates, 2 cookies and 9 cakes 2 bar chocolates, 1 cookies and 6 cakes etc are some purchase patterns where the customer is eligible to get offer Express 'all the purchase patterns where the customer is eligible to get offer as a language L (2 marks) Design a Pushdown Automaton [PDA] M that will recognise language L (6 marks) Justify that the PDAM designed accepts the purchase pattern defined in L (2 marks)